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в FIGURE 7 FIGURE I 40. Find the volume of a pyramid (Figure 8) in terms of its height h and the area A of its base.

в FIGURE 7 FIGURE I 40. Find the volume of a pyramid (Figure 8) in terms of its height h and the area A of its base.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 51AR
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Please solve 40 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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