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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.

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.

Elementary Geometry For College Students, 7e
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
Section9.1: Prisms, Area And Volume
Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...
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Please solve 41 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
Transcribed Image Text: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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