Chapter 8.5, Problem 3QQ

To determine

To find: The volume of the solid cube in inches.

Answer to Problem 3QQ

The volume of a solid circle is $\frac{128}{3}$ .

Explanation of Solution

Given information:

The radius of solid is $2\text{inches}$ . Each cross section perpendicular to a certain diameter is a square with one side lying in the circle.

The volume of a solid circle is determined by taking integral.

Thus,

  $\begin{array}{c}\underset{-2}{\overset{2}{{\displaystyle \int }}}\left(2\cdot \sqrt{4-x^2}\right)dx={{\displaystyle \left(\frac{-4x\left(x^2-12\right)}{3}\right)}}_{-2}^2\\ =\frac{128}{3}\end{array}$ .

Therefore, option C is correct.