To find : The height of
Answer to Problem 7P
The required volume is
Explanation of Solution
Given information :
The pyramid has a base of side
The sphere (S) its center on the base of pyramid (P) and S is tangent to all eight edges of P.
Formula used :
R= base radius
H=height of the spherical segment.
Calculation :
The figure-I shows a cross section of pyramid passing through the top and through two opposite corners of the square base.
Now,
We first observe that the shaded volume is equal to (half the volume of the sphere) − (sum of the four equal volumes cut off by the triangular faces of the pyramid).
To find the volume of four spherical caps we need the distance
We have
Now from similar triangles
Therefore,
So,
So, volume of each cap
Here,
So, required volume is
Chapter 6 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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