# Three tennis balls are packaged in a box as shown below. The box is 12.1 centimeters long, 3.5 centimeters wide, and 3.5 centimeters tall. Each ball is 3.3 centimeters in diameter. What is the volume of the empty space in the box?

May 13, 2018

$91.8 c {m}^{3}$

#### Explanation:

Volume of the box is $12.1 \times 3.5 \times 3.5 = 148.225 c {m}^{3}$

Each ball is $\frac{4}{3} \times \pi \times {1.65}^{3} = 18.8165692 c {m}^{3}$

There are three balls $\implies 56.4497076 c {m}^{3}$

Subtract

$\implies 148.225 - 56.4497076 = 91.7752924 c {m}^{3}$

May 13, 2018

${V}_{\text{empty space}} = 91.775$ $c {m}^{3}$

#### Explanation:

${V}_{\text{box}} = l \cdot w \cdot h = 12.1 \cdot 3.5 \cdot 3.5 = 148.225$ $c {m}^{3}$

${V}_{\text{each ball}} = \frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi {\left(\frac{3.3}{2}\right)}^{3} = \frac{4}{3} \pi \left(\frac{35.937}{8}\right)$ $c {m}^{3}$

${V}_{\text{3 balls}} = \left(\frac{35.937}{2}\right) \pi \approx 56.450$ $c {m}^{3}$

${V}_{\text{empty space}} = 148.225 - 56.450 = 91.775$ $c {m}^{3}$