# How do I find the surface area of a sphere that has a volume of 288 cubic inches?

Jul 4, 2015

The surface area is ${\text{210.90 in}}^{2}$.

#### Explanation:

Here is one way to solve the problem.

The formula for the volume of a sphere is

V = 4/3πr^3

We can solve this for $r$.

3V = 4πr^3 or 4πr^3 = 3V

r^3 = (3V)/(4π)

r^3 = ("3× 288 in"^3)/(4π) = 216/π "in"^3 = "68.7549 in"^3

r = root3("68.7549 in"^3 ) = "4.0967 in"

Now we can insert this value of $r$ into the formula for the area of a sphere.

A = 4πr^2 = 4π × ("4.0967 in")^2 = 4π×"16.2879 in"^2 = "210.90 in"^2 (to two decimal places)