For the following exercises, find the volume of the solid described. 109. The base is the region enclosed by the generic ellipse ( x 2 / a 2 ) + ( y 2 / b 2 ) = 1 . Slices perpendicular to the x -axis are semicircles.
For the following exercises, find the volume of the solid described. 109. The base is the region enclosed by the generic ellipse ( x 2 / a 2 ) + ( y 2 / b 2 ) = 1 . Slices perpendicular to the x -axis are semicircles.
Complete the following problems.
a. Express the area A of the cross-section cut from the ellipsoid
b. Use slices perpendicular to the z-axis to find the volume V of the ellipsoid in part (a).
22
3² 3² 2²
c. Now find the volume of the ellipsoid- 2
abc
=1 by the plane z= d as a function of d. (The area of an ellipse with semiaxes a and b is rab.)
4 25
1. Does your formula give the volume of a sphere of radius a if a = b=c?
Q3: Find the volume of the solid enclosed by the parabola y = x2 + z? and the
cone y = 32 - x2 - z2.
The result of slicing through the center of the solid S is the base described by the ellipse
1. Cross
81
9
sections of S perpendicular to the x-axis and the elliptical base are circles. What is the volume of S? Enter your
answer in terms of r.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY