# A sphere has a volume of 113.04 cubic inches. What is its surface area?

May 21, 2017

The surface area of the sphere is $37.69 {\text{in}}^{2}$

#### Explanation:

in both of these formulas, to find the surface area and the volume of the sphere, they require the radius of the sphere. So we will find the radius of the sphere to find the surface area.

$V = \frac{4 \pi {r}^{3}}{3} = 113.04$

$4 \pi {r}^{3} = 113.04 \times 3$

$4 \pi {r}^{3} = 339.12$

pi r^3 = 339.12 ÷ 4

$\pi {r}^{3} = 84.78$

r^3 = 84.78 ÷ pi

${r}^{3} = 26.986$

$r = \sqrt[3]{26.986}$

color(blue)(r = 2.999

$S A = 4 \pi {r}^{2}$

$S A = 4 \pi {2.999}^{2}$

$S A = \pi {11.998}^{2}$

color(red)(SA = 37.69"in"^2