Chapter 8.3, Problem 51E

a.

To determine

To find : the volume of the solid.

Answer to Problem 51E

The volume of the solid is $\frac{32\pi }{3}$ .

Explanation of Solution

Given information : A round hole is drilled through the centre of a spherical solid of radius $r$ . The resulting cylindrical hole has height $4cm$ .

Calculation :

The volume of the remaining solid can be found by solving the integral:

  $\begin{array}{l}{\displaystyle \underset{-2}{\overset{2}{\int }}\pi \left(4-x^2\right)dx}\\ \Rightarrow \frac{32\pi }{3}\end{array}$

b.

To determine

What is unusual about the answer.

Answer to Problem 51E

The result does not depend on the radius $r$ .

Explanation of Solution

Given information : A round hole is drilled through the centre of a spherical solid of radius $r$ . The resulting cylindrical hole has height $4cm$ .

From the above information it is observed that the result does not depend on the radius $r$ .