Chapter 12.4, Problem 21PPS

To determine

To find:

The volume of the empty space in the box.

Answer to Problem 21PPS

The volume of the empty space is $\text{521}{\text{.5 cm}}^3$ .

Explanation of Solution

Given information:

  

Calculation:

The required volume of the empty space is the difference of volumes of the rectangular prism and the cylinders.

  $\begin{array}{c}V=V_{prism}-V_{cylinder}\\ =\left(9\right)\left(18\right)\left(15\right)-2\left[\pi {\left(4.5\right)}^2\left(15\right)\right]\\ =2430-607.5\pi \\ \approx 521.5{\text{ cm}}^3\end{array}$

Hence the volume of the empty space is $\text{521}{\text{.5 cm}}^3$ .