Question

A cylindrical container of three rubber balls has a height of $18$ centimeters and a diameter of $6$ centimeters. Each ball in the container has a radius of $3$ centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.

Answer 1

Step 1:Volume of cylindrical container

Given,

Height of cylinder $=18cm$

Diameter of cylinder $=6cm$

Radius of cylinder = $\frac{6}{2}=3\mathrm{cm}$

Radius of rubber balls = $=3cm$

$$\begin{gathered} =\mathrm{\pi }{\left(\mathrm{r}\right)}^2\mathrm{h}=\mathrm{\pi }{\left(3\right)}^{2}18 \\ =162\mathrm{\pi } \end{gathered}$$

Volume of one ball

$=\frac{4}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3=\frac{4}{3}\mathrm{\pi }{\left(3\right)}^3=36\mathrm{\pi }$

Volume of $3$ balls

$$\begin{gathered} =36\mathrm{\pi }*3 \\ =108\mathrm{\pi } \end{gathered}$$

Step 2: Volume not occupied by balls

$$\begin{gathered} =162\mathrm{\pi }-108\mathrm{\pi } \\ =54\mathrm{\pi } \\ =169.64 \end{gathered}$$

Hence, Volume not occupied by balls $169.64{\mathrm{cm}}^2$