Question

Find the surface area of a sphere with a volume of 36π in3.

Answer 1

First use known volume to solve for radius:
$V=\frac{4}{3}\pi r^{3}$
$r=\sqrt[3]{\frac{3V}{4\pi}}$
$r=\sqrt[3]{\frac{3(36\pi)}{4\pi}}$
$r=\sqrt[3]{27}$
$r=3$

Then use the radius to get the surface area:
$A_{surf}=4 \pi r^{2}$
$A_{surf}=4 \pi 3^{2}$
$A_{surf}=4 \pi 9$
$A_{surf}=36\pi\approx113.09$