What is the surface area to volume ratio of a sphere?

Feb 23, 2016

Surface area to volume ratio of a sphere equals to $\frac{3}{r}$, where $r$ is the sphere's radius.
Surface area of a sphere with radius $r$ equals to $4 \pi {r}^{2}$.
The volume of this sphere is $\frac{4}{3} \pi {r}^{3}$.
$\frac{4 \pi {r}^{2}}{\frac{4}{3} \pi {r}^{3}} = 4 \left(\frac{3}{4}\right) \left(\frac{\pi}{\pi}\right) \left({r}^{2} / {r}^{3}\right) = \frac{3}{r}$