Question

Three tennis balls are stored in a cylindrical container with a height of $8$ inches and a radius of $1.43$ inches.

The circumference of a tennis ball is $8$ inches.

Find the volume of a tennis ball?

Answer 1

The volume of the tennis ball:

The circumference of the tennis ball is $8$ inches.

The tennis ball is the form of sphere whose circumference is given by formula $2\mathrm{\pi r}$, where $r$ is the radius.

Thus, if $r$ is the radius then according to given condition, $2\mathrm{\pi r}=8$ or $r=\frac{8}{2\mathrm{\pi }}$inches.

Now, the volume of the sphere of radius $r$ is $\frac{4}{3}{\mathrm{\pi r}}^3$, hence, find the volume of the given tennis ball by substituting $r=\frac{8}{2\mathrm{\pi }}$inches in $\frac{4}{3}{\mathrm{\pi r}}^3$and simplify:

$$\begin{gathered} \text{Volume}=\frac{4}{3}\pi \times {\left(\frac{8}{2\mathrm{\pi }}\right)}^3 \\ =\frac{4}{3}\times \frac{64}{{\mathrm{\pi }}^2} \\ =8.65{\text{inches}}^3 \end{gathered}$$

Hence, the required volume of the tennis ball is $8.65{\text{inches}}^3$.