Chapter 12.4, Problem 25PPS

To determine

Find the volume of empty space in the box.

Answer to Problem 25PPS

volume of empty space is $140.336c{m}^3$

Explanation of Solution

Given:

Concept Used:

Volume of empty space is calculated as,

  $V=Volumeofrecatngularbox-3\times volumeofaoneball\left(sphere\right)$

Calculation:

Volume of empty space is calculated as,

  $\begin{array}{l}V=Volumeofrecatngularbox-3\times volumeofaoneball\left(sphere\right)\\ V=\left(l\times w\times h\right)-\left(3\right)\left(\frac{4}{3}\pi r^3\right)\\ V=\left(13.1\times 4.5\times 4.5\right)-3\left(\frac{4}{3}\pi r^3\right)\end{array}$

One each ball measures,

diameter $\left(d\right)=4.3cm$

radius $\left(r\right)=\frac{4.3}{2}=2.15cm$

  $\begin{array}{l}V=Volumeofrecatngularbox-3\times volumeofaoneball\left(sphere\right)\\ V=\left(l\times w\times h\right)-\left(3\right)\left(\frac{4}{3}\pi r^3\right)\\ V=\left(13.1\times 4.5\times 4.5\right)-3\left(\frac{4}{3}\times \frac{22}{7}{\left(2.15\right)}^3\right)\\ V=265.275-\frac{874.577}{7}\\ V=265.275-124.939\\ V=140.336c{m}^3\end{array}$

Conclusion:

Thus, volume of empty space is $140.336c{m}^3$