y = 1/x, y = 0, x = 1, x = 4; about the x-axis. find the volume of the solid obtained by rotating the region bounded by y=x^4, y=1, and the y -axis about the line y=-2. Find the volume V of the solid obtained by rotating the region enclosed by the graphs of y = e −x, y = 1 − e −x, and x = 0 about y = 2. Find the volume of the solid obtained by rotating the region bounded by y=x^6, y=1 about the line y=4 asked Sep 15, 2011 in Calculus Answers by anonymous | 1. Find the surface area of this solid S. I've taken a slice perpendicular to the axis of rotation. 0 Volume of the solid from rotating four curves. asked by jimmy on May 4, 2007; Calculus. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Your teacher may ask you to turn in this work. region, the solid, and a typical disk or washer. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. 11 Find the volume of a pyramid with height h = 9 and. Volume = Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x^3 , y=1 , and the y -axis around the y -axis. The concepts of markers and landmarks which define the direction of a journey apply to that of any business. y = 5x, y = 5[itex]\sqrt{x}[/itex] about y = 5. Determine the volume of the solid generated by rotating the region bounded by f (x) x2 4x 5, x 1, x 4 and the x-axis about the x-axis. Dominique S. The two general categories in which all the types of welding can be divided is fusion welding and solid state welding. Find the volume of the solid obtained by rotating the region bounded by y=1/4 (x^2), x=2 and y=0 about the y-axis. Business Model and Strategic Plan Essay For any journey the path must be defined with clear and recognizable details for it to be successful. The two general categories in which all the types of welding can be divided is fusion welding and solid state welding. about y = 1. 11)Find the volume of the solid obtained by rotating the region B in the figure below about the y-axis. Sketch the region, the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Please help me out with the disk. We first find the points of intersection of the equations [math]x=11y[/math] and [math]y. Answer to: Find the volume of the solid obtained by rotating the region bounded by x = 8y^2, y = 1, x = 0, about the y-axis. y^2 = 2x, x = 2y; about the y-axis. find the volume of the solid formed by rotating the region enclosed by y=e^2x , y=0, x=0 , x=0. IPG Photonics Corporation (NASDAQ:IPGP) Q1 2020 Earnings Conference Call May 05, 2020, 10:00 AM ET Company Participants James Hillier - VP of IR Valentin Gapont. About x axis. Question: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves {eq}y = x^2 {/eq} and {eq}y = x^3 {/eq} about the {eq}x {/eq}-axis. Use the method of cylindrical shells to find the volume V. Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. Question: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves {eq}y = x^2 {/eq} and {eq}y = x^3 {/eq} about the {eq}x {/eq}-axis. Sketch the region, the solid, and. Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=8+x^7. 5] Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. Question: Find the volume of the solid obtained by rotating the region bounded by y = x{eq}^{3} {/eq}, y = 1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral. Find the volume of the solid S obtained by rotating the region R around the x-axis. Let R be region bounded by the graph of , and the line y = 3. Find the volume of the solid obtained by rotating the region A in the figure below about the line y=3 Get more help from Chegg Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. Find the volume of the solid obtained by rotating the region bounded by the curves and about the -axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. 1) y=1-x2 y=0 Homework Equations The Attempt at a Solution I sketched a curve. region, the solid, and a typical disk or washer. CHAPTER 1: INTRODUCTION1. Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V= asked by Anonymous on December 2, 2016. Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x and y=x^1/2about the line y=1. y = x + 1, y = 0 , x = 0 , x = 2 ; about the x -axis. Feel free to change the scale of the given graph. asked by jimmy on May 4, 2007; Calculus. Volume=? napoleonpp Apr 29, 2016. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x=7+(y-5)^2, x=8 I have tried integrating from 0 to 8 using the equation (2*pi*y)[7+(y-5)^2] dy but it is not giving me the correct answer. y = 1/x^3, y = 0, x = 2, x = 4; about x = −1" Hi, could anybody give me some direction as how to solve this problem? I know that the integration is with respect to y, but I do not know what the inner and outer radii are. About x axis. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. 10) Find the volume of the solid obtained by rotating the region A in the figure below about the line x = −4. Answer to: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Use the method of cylindrical shells to find the volume V. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 1) y=1-x2 y=0 Homework Equations The Attempt at a Solution I sketched a curve. Find the area of R. The objective of Two Brothers. Volume = Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^3 , y=1 , and the y -axis and whose cross-sections perpendicular to the x axis are semicircles. LABEL YOUR RADII. Do not evaluate the integral. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. Find the volume of solid obtained by rotating the region under the graph of the function f(x)=5x−x2 about the x-axis over the interval [0,5]?. Get an answer for '`y = (1/4)x^2, y = 5 - x^2` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. asked by me on October 31, 2010; calculus. Find the volume of the solid obtained by rotating the region bounded by x = 8y^2, y = 1, x = 0, Question: Find the volume of the solid obtained by rotating the region bounded by {eq}\; x = 8y^2, \; y = 1, \; x = 0, {/eq} about the {eq}y {/eq}-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about. asked by jimmy on May 4, 2007; Calculus. The objective of Two Brothers. Finding the volume of a solid revolution is a method of calculating the volume of a 3D object formed by a rotated area of a 2D space. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. 1) y=1-x2 y=0 Homework Equations The Attempt at a Solution I sketched a curve. Answer to Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. Find the volume of the solid obtained by rotating the region bounded by y=x^4, y=1,and the y-axis around xaxis? Pls correct me - I'm using shell method -> int -1 to 1 2pi(x^4-1)dx = 24pi/5. Hint: Express V as a sum of two integrals. Find the volume of the solid region obtained by rotating the region bounded by from APMA 1110 at University of Virginia. sing the method of cylindrical shells find the volume of the solid obtained by rotating the region bounded by y = ln x, y = 0 and x = 2 about the y-axis. Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3. Homework Equations V= pi* integral [a,b] r^2 The Attempt at a Solution So i used intergral 0 to 2 (2x-x^2)^2 dx this is wat i. Show transcribed image text Find the volume of the solid obtained by rotating the region bounded by the curves y= sin(x), x=pi/2,x=pi and y=0about the x-axis. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. Find the volume of a solid obtained by rotating the region enclosed by the graphs x = 10 – 2y and x = 25 - y2 about the y- axis. Solid of Revolution - Finding Volume by Rotation Finding the volume of a solid revolution is a method of calculating the volume of a 3D object formed by a rotated area of a 2D space. Your teacher may ask you to turn in this work. y = 3 - (5/2)x, y = 0, x = 1, x = 2 for Teachers for Schools for Working Scholars. Volume = Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^3 , y=1 , and the y -axis and whose cross-sections perpendicular to the x axis are semicircles. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. Thx kostyantyn! Rotate the red strip of thickness x about the line x = 3. Question 967112: Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=(pi)/2 about the line y=1 Answer by amarjeeth123(515) (Show Source):. asked by jimmy on May 4, 2007; calculus. Sketch the. Find the volume of the solid obtained by rotating the region enclosed by x=9y, y^3=x, yâ¥0 about the y-axis using the method of disks or washers. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x, y = 5[itex]\sqrt{x}[/itex] about y = 5. Find the volume of a solid obtained by rotating the region enclosed by the graphs x = 10 - 2y and x = 25 - y2 about the y- axis. Added Dec 11, 2011 by mike. We want to determine the volume formed by rotating the area enclosed by [math]x=11y[/math] and [math]y^3=x,[/math] with [math]y \ge 0[/math] about the Y axis. Sketch the region, the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by the given curves about. region, the solid, and a typical disk or washer. They range from the conventional oxyacetylene torch welding to laser welding. y = 1/ x , y = 0 , x = 1, x = 4 ; about the x -axis. Answer to: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Get more help from Chegg Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. 0 SO- O'T-. Find the volume of the solid obtained by rotating the region under the curve y = 1 x + 1 from 0 to 1 about the x -axis. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. Find the surface area of this solid S. Get an answer for '`y = 2 - (1/2)x, y = 0, x = 1, x = 2` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. In this case. Find the volume of the solid obtained by rotating the region bounded by y=10x and y=2x^2 around the x-axis. Feel free to change the scale of the given graph. Finding volume of a solid of revolution using a washer method. Find the volume of the solid region obtained by rotating the region bounded by from APMA 1110 at University of Virginia. Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V= asked by Anonymous on December 2, 2016. y = x + 1, y = 0 , x = 0 , x = 2 ; about the x -axis. Find the volume of the solid obtained by rotating the region bounded by y=x^4, y=1,and the y-axis around xaxis? Pls correct me - I'm using shell method -> int -1 to 1 2pi(x^4-1)dx = 24pi/5. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. The fusion welding process involves chemical bonding. Find the volume of the solid obtained by rotating the region bounded by the given? First graph the situation and verify that the volume is integral (from 0 to 1) of pi(9x^2)^2 dx Then it is pi81x^5/5 now substitute 1 and 0 and subract V = 81pi /5 OK!. We will rotate the area bounded by the two curves and the y-axis. xy=1, y=0, x=1, x=2; about x=-1 Found 2 solutions by richard1234, Edwin McCravy:. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Question 3: Find the volume of the solid formed by rotating the region enclosed by y = x^6, y=1 about the line y=4 If you could help me with any one of these, it would be amazingg. In this case. Find the volume of the solid obtained by rotating the region. F(x) should be the "top" function and min/max are the limits of integration. 30B Volume Solids 4 EX 1 Find the volume of the solid of revolution obtained by revolving the region bounded by , the x-axis and the line x=9 about the x-axis. asked by jimmy on May 4, 2007; calculus. Sketch the region, the solid, and a typical disk or washer. Show transcribed image text Find the volume of the solid obtained by rotating the region bounded by the curves y= sin(x), x=pi/2,x=pi and y=0about the x-axis. Sketch the region, the solid, and a typical disk or "washer. y=2-(1/2)x, y=0, x=1, x=2 17. You just studied 7 terms! Now up your study game with Learn mode. Business Model and Strategic Plan Essay For any journey the path must be defined with clear and recognizable details for it to be successful. Here is a graph of the region. Answer to: Find the volume of the solid obtained by rotating the region bounded by the curves y = 1 / x^5, y = 0, x = 3, x=4 about the line x. Feel free to change the scale of the given graph. bounded by the given curves about the specifed line. We want to use the disc method, but our discs. Sketch the region, the solid, and a typical disk or washer. asked by jimmy on May 4, 2007; calculus. Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. For a function rotated about the x-axis, the volume is given by \pi \int_a^b f^2(x) dx. The solid produced when rotating this region about the line [math]y=7[/math], when cut perpendicular to the x-axis, has cross sections that look like "washers", or circles. Find the volume of the solid obtained by rotating the region bounded by the curves y = 1 / x^5, Question: Find the volume of the solid obtained by rotating the region bounded by the curves {eq}y = 1 / x^5, y = 0, x = 3, x=4 {/eq} about the line {eq}x = -3 {/eq}. y = 5x, y = 5[itex]\sqrt{x}[/itex] about y = 5. The objective of Two Brothers. We want to use the disc method, but our discs. The thickness of the slice is dy, so we need the equations in the form x = a function of y. y=2-(1/2)x, y=0, x=1, x=2 17. Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. In this case. Do not evaluate the integral. 9 about the x-axis. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. The fusion welding process involves chemical bonding. Y = 1 + Sec(x), Sxs Y = 3; About Y = 1 Sketch The Region. x= 4y^2 , x = 4 Find the volume V of this. " (Do this on paper. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9x^2, y = 9x, x ≥ 0; about the x-axis. 1) y=1-x2 y=0 Homework Equations The Attempt at a Solution I sketched a curve. asked by Anonymous on January 30, 2020; calculus. The slice is taken at a variable value of y. sing the method of cylindrical shells find the volume of the solid obtained by rotating the region bounded by y = ln x, y = 0 and x = 2 about the y-axis. Question: Find the volume of the solid obtained by rotating the region bounded by y = x{eq}^{3} {/eq}, y = 1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral. y = 3e^(-x), y = 3,. 0 Volume of the solid from rotating four curves. Finding the volume of a solid revolution is a method of calculating the volume of a 3D object formed by a rotated area of a 2D space. Homework Statement Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^2 y=2x about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. 11 Find the volume of a pyramid with height h = 9 and. Find the volume of the solid obtained by rotating the region. y2 = 2x, x= 2y Please state your chosen method (washer or shell): Integral: Volume:. Added Dec 11, 2011 by mike. Sketch the region, the solid, and. We can find Volume [math]V[/math] of a solid obtained by rotation of a region in the [math]x[/math],[math]y[/math]-plane through a line of symmetry. About x axis. Sketch the region, the solid, and a typical disk or washer for y = x^3, y=1, x=2; about y=-3. Let R be the region enclosed by f(x) = x2 + 4, g(x) = (x - 3) and the axes x = 0 and y = 0. Sketch the region, the solid, and a typical disk or washer. Below is a graph of the bounded region. They range from the conventional oxyacetylene torch welding to laser welding. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. Find the volume V of the solid obtained by rotating the region bounded by the from MATH 125 at University of Washington, Tacoma. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. Do not evaluate the integral. In this case. Question 967112: Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=(pi)/2 about the line y=1 Answer by amarjeeth123(515) (Show Source):. Finding volume of a solid of revolution using a washer method. What am I doing wrong?. y^2 = 2x, x = 2y; about the y-axis. Please read the FAQ before posting. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. In this video I show you how to find the volume of a solid obtained by rotating the region between a parabola and a cubic function about the y-axis. The concepts of markers and landmarks which define the direction of a journey apply to that of any business. I've taken a slice perpendicular to the axis of rotation. The two general categories in which all the types of welding can be divided is fusion welding and solid state welding. " (Do this on paper. Homework Equations V= pi* integral [a,b] r^2 The Attempt at a Solution So i used intergral 0 to 2 (2x-x^2)^2 dx this is wat i. We will first determine the points of intersection of these two lines so as to. sing the method of cylindrical shells find the volume of the solid obtained by rotating the region bounded by y = ln x, y = 0 and x = 2 about the y-axis. asked by Anonymous on January 30, 2020; calculus. Answer Save. Find the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis using the method of your choice. $ y = x $ , $ y = 0 $ , $ x = 2 $ , $ x = 4 $ ; about $ x = 1 $. y = 9x^2, y = 9x, x ≥ 0; about the x-axis. Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=3x about the line x=3 using the method of disks or washers. Find volume of solid when rotating on x-axis and find volume of solid when rotating on y-axis with the same equation. Find the volume of the solid obtained by rotating the region enclosed by the curves f(x) = x^2 + 1 and g(x)=51-x^{2} about the x-axis. Sketch the region, the solid, and a typical disk or washer. Please round the answers to the nearest hundredth. using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=e^x, y=0, x=-2, and x=1 about the x-axis. Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V= asked by Anonymous on December 2, 2016. Question: Find the volume of the solid obtained by rotating the region bounded by {eq}y=x^2, \ \ y=6x, {/eq} about the line {eq}x=6 {/eq} using the following methods. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Graph, set up and simplify the integral, evaluate. If you have any questions or suggestions regarding the sub, please send the us (the moderators) a message. of the boundary of this solid. 11)Find the volume of the solid obtained by rotating the region B in the figure below about the y-axis. Sketch the. (Use a graphing calculator. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 1/ x , y = 0 , x = 1, x = 4 ; about the x -axis. y = 1/x, y = 0, x = 1, x = 4; about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. x = 7y2, x = 7; about x = 7 Guest Feb 1, 2017 0 users composing answers. Find the volume of the solid obtained by rotating the region bounded by and x = 1 about the line x = 1. 12) Find the volume of the solid obtained by rotating the region B in the figure below about the line x = 6. asked • 05/31/16 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. The volume of the solid obtained by rotating a region about a specific line from a to b is given by. Below is a graph of the bounded region. 5 10 Sketch The Solid, And A Typical Disk Or Washer. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. `x = y^2, x = 1 - y^2` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Question: Find The Volume V Of The Solid Obtained By Rotating The Region Bounded By The Given Curves About The Specified Line. Answer to: Find the volume of the solid obtained by rotating the region bounded by the curves y = sin(x), x = pi/2, x = pi, and y = 0 about the. y=2-(1/2)x, y=0, x=1, x=2 17. Homework Statement Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. The volume of a solid of revolution can be determined by integrating the area of the circles created by the revolution. Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. Thanks! :B. Feel free to change the scale of the given graph. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. y = sin x, y =cos x, 0 ≤ x ≤ π /4; about y = ‒1. Find the volume of a solid obtained by rotating the region enclosed by the graphs x = 10 - 2y and x = 25 - y2 about the y- axis. Answer to: Find the volume of the solid obtained by rotating the region bounded by the curves y = sin(x), x = pi/2, x = pi, and y = 0 about the. Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V= asked by Anonymous on December 2, 2016. The volume of the solid obtained by rotating a region about a specific line from a to b is given by. Added Dec 11, 2011 by mike. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Please round the answers to the nearest hundredth. Sketch the region, the solid, and a typical disk or washer. asked • 05/31/16 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=8+x^7. We can find Volume [math]V[/math] of a solid obtained by rotation of a region in the [math]x[/math],[math]y[/math]-plane through a line of symmetry. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. Sketch the region, the solid, and a typical disk or washer. Question: Find the volume of the solid obtained by rotating the region bounded by y = x{eq}^{3} {/eq}, y = 1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral. Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. asked by Anonymous on January 30, 2020; calculus. I get this as wrong # 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis using the method of your choice. Find volume of solid when rotating on x-axis and find volume of solid when rotating on y-axis with the same equation. 7k views shell method. Find the volume of the solid obtained by rotating the region. y2 = 2x, x= 2y Please state your chosen method (washer or shell): Integral: Volume:. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region enclosed by x=9y, y^3=x, yâ¥0 about the y-axis using the method of disks or washers. x= 4y^2 , x = 4 Find the volume V of this. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region bounded by and x = 1 about the line x = 1. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. 11)Find the volume of the solid obtained by rotating the region B in the figure below about the y-axis. x=2sqrt(y), x= 0, y= 9; about the y- axis. Please round the answers to the nearest hundredth. Find the volume of the solid obtained by rotating the region bounded by the given curves about. Find the formula for the volume of the solid obtained by rotating the region from MA 1660 at Purdue University. Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. Find the volume of the solid obtained by rotating the region. y=sqrt(25-x 2) y=0 x=2 x=4 Homework Equations The Attempt at a Solution I drew a graph, region and solid. You just studied 7 terms! Now up your study game with Learn mode. Here is a graph of the region. y = 9x^2, y = 9x, x ≥ 0; about the x-axis. Sketch the region, the solid, and a typical disk or washer. There was an error in the earlier version of the solution with the upper bound of y value. About x axis. Question: Find the volume of the solid obtained by rotating the region bounded by {eq}y=x^2, \ \ y=6x, {/eq} about the line {eq}x=6 {/eq} using the following methods. Here are both of these sketches. How do you find the volume of the bounded region if #y = sinx#, #y = 0# from #x = pi/4#, #x = 3pi/4#, revolved around the y-axis? Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. `x = y^2, x = 1 - y^2` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. 30B Volume Solids 4 EX 1 Find the volume of the solid of revolution obtained by revolving the region bounded by , the x-axis and the line x=9 about the x-axis. In this case. This widget will find the volume of rotation between two curves around the x-axis. Get an answer for '`y = (1/4)x^2, y = 5 - x^2` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. find the volume of the solid obtained by rotating the region bounded by y=x^4, y=1, and the y -axis about the line y=-2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer for y = x^3, y=1, x=2; about y=-3. 8) Find the volume of the solid obtained by rotating the region A in the figure below about the line y = −7. Question: Find the volume of the solid obtained by rotating the region bounded by {eq}y=x^2, \ \ y=6x, {/eq} about the line {eq}x=6 {/eq} using the following methods. Do not evaluate the integral. F(x) should be the "top" function and min/max are the limits of integration. Feel free to change the scale of the given graph. Sketch the. Find the volume of the solid obtained by rotating the region about the x-axis 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis using the method of your choice. Answer to: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x^2 , x=y^2; about y=1 Why is the area: A(x)=Pi[(1-x^2)^2-(1. x=2sqrt(y), x= 0, y= 9; about the y- axis. The fusion welding process involves chemical bonding. About x axis. They range from the conventional oxyacetylene torch welding to laser welding. Business Model and Strategic Plan Essay For any journey the path must be defined with clear and recognizable details for it to be successful. IPG Photonics Corporation (NASDAQ:IPGP) Q1 2020 Earnings Conference Call May 05, 2020, 10:00 AM ET Company Participants James Hillier - VP of IR Valentin Gapont. `x = y^2, x = 1 - y^2` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. 11)Find the volume of the solid obtained by rotating the region B in the figure below about the y-axis. If you could show me the steps as well, that'd be appreciated. bounded by the given curves about the specifed line. 12) Find the volume of the solid obtained by rotating the region B in the figure below about the line x = 6. Find volume of solid when rotating on x-axis and find volume of solid when rotating on y-axis with the same equation. Let R be region bounded by the graph of , and the line y = 3. Here are both of these sketches. LABEL YOUR RADII. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. The volume of a solid of revolution can be determined by integrating the area of the circles created by the revolution. Answer to: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. Answer to Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis? I have another question too. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. The two general categories in which all the types of welding can be divided is fusion welding and solid state welding. asked by jimmy on May 4, 2007; Calculus. Sketch the region, the solid, and a typical disk or washer. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Since we a rotating around the y axis using the method of shells we integrate with respect to x. The volume of the resulting solid is PLEASE HELP!!!!. y = 6 x^6 , y = 6 x , x >= 0 Find the volume V of this solid. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region enclosed by the curves f(x) = x^2 + 1 and g(x)=51-x^{2} about the x-axis. 0 SO- O'T-. 8 Find the volume of the solid obtained by rotating the region bounded by and about the line x = 1. of the boundary of this solid. By signing up, you'll. Sketch the region, the solid, and a typical disk or washer. About x axis. y = 1/x^3, y = 0, x = 2, x = 4; about x = −1" Hi, could anybody give me some direction as how to solve this problem? I know that the integration is with respect to y, but I do not know what the inner and outer radii are. This is an extension of the disc method. We want to determine the volume formed by rotating the area enclosed by [math]x=11y[/math] and [math]y^3=x,[/math] with [math]y \ge 0[/math] about the Y axis. Sketch the region, the solid. Find the volume of the solid obtained by rotating the region enclosed by the lines… 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis? I have another question too. Find the volume of the solid obtained by rotating the region bounded by the curves and about the -axis. If you could show me the steps as well, that'd be appreciated. Use the method of cylindrical shells to find the volume V. F(x) should be the "top" function and min/max are the limits of integration. y = 3e^(-x), y = 3,. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. find the volume of the solid formed by rotating the region enclosed by y=e^2x , y=0, x=0 , x=0. Get more help from Chegg Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. 0 Volume of the solid from rotating four curves. Compute the volume V obtained by rotating R about the x-axis. Question: Find the volume of the solid obtained by rotating the region bounded by {eq}y=x^2, \ \ y=6x, {/eq} about the line {eq}x=6 {/eq} using the following methods. Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0. In this video I show you how to find the volume of a solid obtained by rotating the region between a parabola and a cubic function about the y-axis. Hint: Express V as a sum of two integrals. 7k views shell method. IPG Photonics Corporation (NASDAQ:IPGP) Q1 2020 Earnings Conference Call May 05, 2020, 10:00 AM ET Company Participants James Hillier - VP of IR Valentin Gapont. If you could show me the steps as well, that'd be appreciated. We will rotate the area bounded by the two curves and the y-axis. molisani in Mathematics. Find the volume of the solid obtained by rotating the region bounded by the curves and about the -axis. Your teacher may ask you to turn in this work. 5] Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by y=x^4, y=1,and the y-axis around xaxis? Pls correct me - I'm using shell method -> int -1 to 1 2pi(x^4-1)dx = 24pi/5. LABEL YOUR RADII. Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and y^2=x about the x-axis. There are multiple ways to solve this, but I will use the "washers" method. Please read the FAQ before posting. The thickness of the slice is dy, so we need the equations in the form x = a function of y. y=x^2 , x=y^2; about y=1 Why is the area: A(x)=Pi[(1-x^2)^2-(1. Sketch the region, the solid, and a typical disk or washer. A place to ask questions, give advice and discuss the mathematical field of calculus. Feel free to change the scale of the given graph. The volume of the resulting solid is PLEASE HELP!!!!. Please round the answers to the nearest hundredth. I get this as wrong # 2. F(x) should be the "top" function and min/max are the limits of integration. 9 Find the volume of a right circular cone with height h = 15 and base radius r = 2. Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 6 x^6 , y = 6 x , x >= 0 Find the volume V of this solid. Volume = Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x^3 , y=1 , and the y -axis around the y -axis. 5 10 Sketch The Solid, And A Typical Disk Or Washer. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. y=sqrt(25-x 2) y=0 x=2 x=4 Homework Equations The Attempt at a Solution I drew a graph, region and solid. Answer to: Find the volume of the solid obtained by rotating the region bounded by x = 8y^2, y = 1, x = 0, about the y-axis. Graph, set up and simplify the integral, evaluate. Sketch the region, the solid, and a typical disk or washer. Question: Find The Volume V Of The Solid Obtained By Rotating The Region Bounded By The Given Curves About The Specified Line. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. y = 1/ x , y = 0 , x = 1, x = 4 ; about the x -axis. In other words we will restrict ourselves to the region in the first quadrant. asked by jimmy on May 4, 2007; calculus. Find the surface area of this solid S. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. In this video I show you how to find the volume of a solid obtained by rotating the region between a parabola and a cubic function about the y-axis. Question: Find the volume of the solid obtained by rotating the region bounded by y = x{eq}^{3} {/eq}, y = 1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral. Y = 1 + Sec(x), Sxs Y = 3; About Y = 1 Sketch The Region. Do not evaluate the integral. molisani in Mathematics. LABEL YOUR RADII. y = sin x, y =cos x, 0 ≤ x ≤ π /4; about y = ‒1. CHAPTER 1: INTRODUCTION1. Find the volume of the solid obtained by rotating the region bounded by y = y2 + 2, y = 2, y = 6, and x = 0, about the y-axis. This may seem complicated, but after a few examples the method will be much clearer. We want to determine the volume formed by rotating the area enclosed by [math]x=11y[/math] and [math]y^3=x,[/math] with [math]y \ge 0[/math] about the Y axis. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. Find the volume V of the solid obtained by rotating the region bounded by the from MATH 125 at University of Washington, Tacoma. Find the volume of the solid obtained by rotating the region bounded by the curves and about the -axis. 11)Find the volume of the solid obtained by rotating the region B in the figure below about the y-axis. find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis? I have another question too. y = 1 + sec x,-pi/3 <= x <= pi/3. The concepts of markers and landmarks which define the direction of a journey apply to that of any business. Dominique S. 9 about the x-axis. Find the volume of the solid obtained by rotating the region bounded by x = 8y^2, y = 1, x = 0, Question: Find the volume of the solid obtained by rotating the region bounded by {eq}\; x = 8y^2, \; y = 1, \; x = 0, {/eq} about the {eq}y {/eq}-axis. Compute the volume V obtained by rotating R about the x-axis. Thx kostyantyn! Rotate the red strip of thickness x about the line x = 3. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. Find the volume V of the solid obtained by rotating the region bounded by the given curves Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Show transcribed image text Find the volume of the solid obtained by rotating the region bounded by the curves y= sin(x), x=pi/2,x=pi and y=0about the x-axis. 8 Find the volume of the solid obtained by rotating the region bounded by and about the line x = 1. Answer to Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. y = 3 - (5/2)x, y = 0, x = 1, x = 2 for Teachers for Schools for Working Scholars. Find the volume of the solid obtained by rotating the region bounded by the given curves about. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. y = x + 1, y = 0 , x = 0 , x = 2 ; about the x -axis. 11 Find the volume of a pyramid with height h = 9 and. Volume=? napoleonpp Apr 29, 2016. Feel free to change the scale of the given graph. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = sin x, y =cos x, 0 ≤ x ≤ π /4; about y = ‒1. y = x + 1, y = 0 , x = 0 , x = 2 ; about the x -axis. Business Model and Strategic Plan Essay For any journey the path must be defined with clear and recognizable details for it to be successful. Find the volume of the solid obtained by rotating the region bounded by the curves and about the -axis. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. y=x^2 y=0 x=3 about the y-axis Jul 02 2015 01:18 PM 1 Approved Answer. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. This is an extension of the disc method. We can find Volume [math]V[/math] of a solid obtained by rotation of a region in the [math]x[/math],[math]y[/math]-plane through a line of symmetry. About x axis. Sketch the region, the solid, and a typical disk or washer. Answer to: Find the volume of the solid obtained by rotating the region bounded by the curves y = sin(x), x = pi/2, x = pi, and y = 0 about the. Find the volume V of the solid obtained by rotating the region bounded by the given curves Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 0 Volume of the solid from rotating four curves. Thx kostyantyn! Rotate the red strip of thickness x about the line x = 3. Find the volume of the solid obtained by rotating the region under the curve y = 1 x + 1 from 0 to 1 about the x -axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Get more help from Chegg Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. We want the volume of the solid formed by rotating the region inside the first quadrant enclosed by the lines [math]y=x^2[/math] and [math]y=5x[/math] about the X-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about. IPG Photonics Corporation (NASDAQ:IPGP) Q1 2020 Earnings Conference Call May 05, 2020, 10:00 AM ET Company Participants James Hillier - VP of IR Valentin Gapont. 5 10 Sketch The Solid, And A Typical Disk Or Washer. How do you find the volume of the bounded region if #y = sinx#, #y = 0# from #x = pi/4#, #x = 3pi/4#, revolved around the y-axis? Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. LABEL YOUR RADII. Added Dec 11, 2011 by mike. 09db3956-4112-3e44-b7e8-f16172a0e38b___a 3. find the volume of the solid formed by rotating the region enclosed by y=e^2x , y=0, x=0 , x=0. bounded by the given curves about the specifed line. y = 5 8 x2, y = 13 0. Sketch the region, the solid, and a typical disk or washer. region, the solid, and a typical disk or washer. 10) Find the volume of the solid obtained by rotating the region A in the figure below about the line x = −4. about y = 1. y = x + 1, y = 0 , x = 0 , x = 2 ; about the x -axis. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y= x 3, y=1 , and the y -axis about the line y=−3. Show transcribed image text Find the volume of the solid obtained by rotating the region bounded by the curves y= sin(x), x=pi/2,x=pi and y=0about the x-axis. This may seem complicated, but after a few examples the method will be much clearer. Find the volume of the solid obtained by rotating the region. 8 Find the volume of the solid obtained by rotating the region bounded by and about the line x = 1. $ y = x $ , $ y = 0 $ , $ x = 2 $ , $ x = 4 $ ; about $ x = 1 $. LABEL YOUR RADII. If you could show me the steps as well, that'd be appreciated. You just studied 7 terms! Now up your study game with Learn mode. In this video I show you how to find the volume of a solid obtained by rotating the region between a parabola and a cubic function about the y-axis. Sketch the region, the solid. Sketch the region, the solid, and a typical disk or washer. 9 about the x-axis. How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y= x, #y = sqrt(x)#; about x = 2? Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. x = 7y2, x = 7; about x = 7 Guest Feb 1, 2017 0 users composing answers. y2 = 2x, x= 2y Please state your chosen method (washer or shell): Integral: Volume:. Find the volume of the solid obtained by rotating the region about the x-axis 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. About x axis. Answer to Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about. 11 Find the volume of a pyramid with height h = 9 and. x= 4y^2 , x = 4 Find the volume V of this. x=2sqrt(y), x= 0, y= 9; about the y- axis. Find the volume of the solid obtained by rotating the region enclosed by the curves f(x) = x^2 + 1 and g(x)=51-x^{2} about the x-axis. Since we a rotating around the y axis using the method of shells we integrate with respect to x. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. The fusion welding process involves chemical bonding. y=x^2 , x=y^2; about y=1 Why is the area: A(x)=Pi[(1-x^2)^2-(1. If you could show me the steps as well, that'd be appreciated. napoleonpp Apr 28, 2016 0 users composing answers. sing the method of cylindrical shells find the volume of the solid obtained by rotating the region bounded by y = ln x, y = 0 and x = 2 about the y-axis. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. The objective of Two Brothers. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region bounded by y=1/4 (x^2), x=2 and y=0 about the y-axis. Graph, set up and simplify the integral, evaluate. 0 SO- O'T-. Determine the volume of the solid generated by rotating the region bounded by f (x) x2 4x 5, x 1, x 4 and the x-axis about the x-axis. 11 Find the volume of a pyramid with height h = 9 and. Find the volume of the solid S obtained by rotating the region R around the x-axis. Find volume of solid (same as number 1). I've taken a slice perpendicular to the axis of rotation. Get more help from Chegg Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. Sketch the region, the solid,…. In other words we will restrict ourselves to the region in the first quadrant. Solid of Revolution - Finding Volume by Rotation. We want to use the disc method, but our discs. If you have any questions or suggestions regarding the sub, please send the us (the moderators) a message. Business Model and Strategic Plan Essay For any journey the path must be defined with clear and recognizable details for it to be successful. y = 3e^(-x), y = 3,. y = sin x, y =cos x, 0 ≤ x ≤ π /4; about y = ‒1. napoleonpp Apr 28, 2016 0 users composing answers. A place to ask questions, give advice and discuss the mathematical field of calculus. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. IPG Photonics Corporation (NASDAQ:IPGP) Q1 2020 Earnings Conference Call May 05, 2020, 10:00 AM ET Company Participants James Hillier - VP of IR Valentin Gapont. Let R be the region enclosed by f(x) = x2 + 4, g(x) = (x – 3) and the axes x = 0 and y = 0. Question: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves {eq}y = x^2 {/eq} and {eq}y = x^3 {/eq} about the {eq}x {/eq}-axis. Homework Statement Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^2 y=2x about the x-axis. I've taken a slice perpendicular to the axis of rotation. y = x + 1, y = 0 , x = 0 , x = 2 ; about the x -axis. About x axis. sing the method of cylindrical shells find the volume of the solid obtained by rotating the region bounded by y = ln x, y = 0 and x = 2 about the y-axis. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. How do you find the volume of the bounded region if #y = sinx#, #y = 0# from #x = pi/4#, #x = 3pi/4#, revolved around the y-axis? Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. Find the volume of the solid obtained by rotating the region bounded by y=1/4 (x^2), x=2 and y=0 about the y-axis. Business Model and Strategic Plan Essay For any journey the path must be defined with clear and recognizable details for it to be successful. This may seem complicated, but after a few examples the method will be much clearer. Added Dec 11, 2011 by mike. This may seem complicated, but after a few examples the method will be much clearer. Answer to Find the volume of the solid obtained by rotating the region A in the figure below about the x-axis. The volume of a solid of revolution can be determined by integrating the area of the circles created by the revolution. We need detailed plans and objectives as well as landmarks and directions we would like the business to travel. F(x) should be the "top" function and min/max are the limits of integration. asked by Anonymous on January 30, 2020; calculus. Feel free to change the scale of the given graph. Hint: Express V as a sum of two integrals. In other words we will restrict ourselves to the region in the first quadrant. Find the volume of the solid obtained by rotating about the line x = 1 the region under the curve y = x 1 − x 2 , 0 ≤ x ≤ 1. Find the volume of the solid obtained by rotating the region about the x-axis 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. find the volume of the solid formed by rotating the region enclosed by y=e^2x , y=0, x=0 , x=0. Then use this information to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by these curves. How do you find the volume of the bounded region if #y = sinx#, #y = 0# from #x = pi/4#, #x = 3pi/4#, revolved around the y-axis? Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. x2, y = 13. LABEL YOUR RADII.
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