Question

Is it possible for a sphere to have the same numerical value for the surface area and volume? Find the radius of a sphere.

Answer 1

Since the surface area is
\[ A = 4\pi*r^2 \]
and the volume is
\[ V = \frac{4}{3}\pi*r^3, \]
and want these quantities to be equal we get
\[ 4\pi*r^2 = \frac{4}{3}\pi*r^3. \]
We cancel 4πr^2 from both sides and get
\[ 1 = \frac{1}{3}*r \]
which means that r=3.

Answer 2

We also have the degenerate case of r=0, but that's pretty uninteresting.