(c) An ellipsoid is given by the equation 4x2 + 4y²+z² = 16;(i)Sketch the three-dimensional (3D) graph of an ellipsoid and its projection on asuitable plane.(ii)Find the volume of the ellipsoid using triple integrals by changing it to thecylindrical coordinate system.

Volume of the ellipsoid, using cylindrical coordinates

Answered: (c) An ellipsoid is given by the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 24E

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. A pool, when viewed from above, is in the shape of an ellipse whose equation is given by (x ^ 2)/144 + (y ^ 2)/49 = 1 A) solve the given equation for y B) Use integration techniques from chapter 5 and/or 7 to compute the area of the ellipse. Hint: Compute the area of the part of the ellipse in quadrant I. Then, multiply your answer by 4 to get the area of the entire ellipse. The units for the area in this problem are in f * t ^ 2 C) Suppose the pool is 10 feet deep and has the shape of an ellipse throughout (an elliptical cylinder). Further, suppose the pool currently has 9 feet of water. Find the work done to pump all of the water out of the pool To do this, first set this up as a Riemann sum, finding the work W_{i} required to pump the slice of water, of width Delta*x out of the pool. Then, set up the corresponding integral and integrate to find the work done to pump all of the water out of the pool. Use the fact that water weights 62.5 lbs / f * t ^ 3
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(c) An ellipsoid is given by the equation 4x2 + 4y²+z² = 16; %3D (i) Sketch the three-dimensional (3D) graph of an ellipsoid and its projection on a suitable plane. (ii) Find the volume of the ellipsoid using triple integrals by changing it to the cylindrical coordinate system.