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