# A sphere has a volume of 288pi. What is the radius?

Dec 17, 2015

$r = 6$

#### Explanation:

The volume of a sphere can be found through the equation

$V = \frac{4}{3} \pi {r}^{3}$

We know that $V = 288 \pi$, so

$288 \pi = \frac{4}{3} \pi {r}^{3}$

Isolate $r$.

$\frac{288 \pi}{\pi} = \frac{\frac{4}{3} \pi {r}^{3}}{\pi}$

$288 = \frac{4}{3} {r}^{3}$

$\frac{3}{4} \times 288 = \frac{3}{4} \times \frac{4}{3} {r}^{3}$

$216 = {r}^{3}$

$\sqrt[3]{216} = r$

$r = 6$

Jan 31, 2016

$r = 6$

#### Explanation:

Volume of Sphere$= \frac{4}{3} \pi {r}^{3}$

So,$288 \pi = \frac{4}{3} \pi {r}^{3}$

$\rightarrow \frac{288 \pi}{\pi} = \frac{4}{3} {r}^{3}$

$\rightarrow 288 = \frac{4}{3} {r}^{3}$

$\rightarrow 288 \div \frac{4}{3} = {r}^{3}$

$\rightarrow 288 \cdot \frac{3}{4} = {r}^{3}$

$\rightarrow 216 = {r}^{3}$

$\rightarrow r = \sqrt[3]{216} = 6$