Question

The volume of a sphere is 2304pi in^3 the radius of the sphere is ___ inches.

Answer 1

The radius = 12 inches.​

Step-by-step explanation:

Given a sphere with radius, r units:

`\text{Volume}=(4)/(3)\pi r^3`

If the volume of a sphere is 2304π in³, then:

`(4)/(3)\pi r^3=2304\pi`

We solve the equation for r:

`\begin{gathered} (4\pi r^3)/(3)=2304\pi \\ 4\pi r^3=2304\pi*3 \\ r^3=(2304\pi*3)/(4\pi) \\ r^3=1728 \end{gathered}`

Next. take cube roots of both sides.

`\begin{gathered} r=\sqrt[3]{1728} \\ r=12\text{ inches} \end{gathered}`

The radius of the sphere is 12 inches.​