Question

find the radius of a sphere if its volume is $\frac{32pi}{3}$ cu in.
8 in.
2 in.
4 in.
$\frac{4}{3}$ in.

Explanation:

Step1: Recall volume formula for sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$, where $V$ is the volume and $r$ is the radius.

Step2: Substitute given volume

We are given that $V=\frac{32\pi}{3}$, so $\frac{4}{3}\pi r^{3}=\frac{32\pi}{3}$.

Step3: Solve for $r^{3}$

First, cancel out $\frac{\pi}{3}$ on both sides of the equation. We get $4r^{3}=32$. Then divide both sides by 4, so $r^{3} = 8$.

Step4: Find $r$

Take the cube - root of both sides. Since $\sqrt[3]{r^{3}}=r$ and $\sqrt[3]{8}=2$, we have $r = 2$ in.

Answer:

2 in.