Please solve 39 only with detailed explanation 39. (a) Figure 7 shows a solid with a circular base of radius a. Each planeperpendicular to the diameter AB intersects the solid in a square.Express the volume of the solid as an integral, and evaluate it.(b) Same problem if each plane intersects the solid in an equilateraltriangle.BFIGURE 7FIGURE40. Find the volume of a pyramid (Figure 8) in terms of its height h and thearea A of its base.41. Find the volume of the solid which is the intersection of the two cylin-ders in Figure 9. Hint: Find the intersection of this solid with eachhorizontal plane.42. (a) Prove that the surface area of a sphere of radius r is 4ar.(b) Prove, more generally, that the area of the portion of the sphereFICURE 910

Given two solids with a circular base of radius a. To find the volumes of the solids.

Answered: Please solve 39 only with detailed…

Math

Geometry

Please solve 39 only with detailed explanation

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 7E: The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of...

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Question

Please solve 39 only with detailed explanation

39. (a) Figure 7 shows a solid with a circular base of radius a. Each plane
perpendicular to the diameter AB intersects the solid in a square.
Express the volume of the solid as an integral, and evaluate it.
(b) Same problem if each plane intersects the solid in an equilateral
triangle.
B
FIGURE 7
FIGURE
40. Find the volume of a pyramid (Figure 8) in terms of its height h and the
area A of its base.
41. Find the volume of the solid which is the intersection of the two cylin-
ders in Figure 9. Hint: Find the intersection of this solid with each
horizontal plane.
42. (a) Prove that the surface area of a sphere of radius r is 4ar.
(b) Prove, more generally, that the area of the portion of the sphere
FICURE 9
10

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