Question

Find the volume of the sphere. Express your answer as an mixed number

Answer 1

Given the circumference is 40π feet, we can find the radius of the sphere. Shown below:

$\begin{gathered} C=2\pi r \\ 40\pi=2\pi r \\ r=\frac{40\pi}{2\pi} \\ r=20 \end{gathered}$

The radius is 20 feet.

Let's put this value into the volume of a sphere formula,

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\pi(20)^3 \\ V=\frac{32000}{3}\pi\text{ ft\textasciicircum{}}3 \end{gathered}$Final Answer$V=\frac{32,000}{3}\pi\text{ cubic feet}$