Question

If the ratio of volume to total surface area of a solid sphere is 8 : 1, then find the radius of the sphere.

Answer 1

Consider a sphere of radius 'r'.
Volume of the sphere $=\frac{4}{3}\pi r^3$
Total surface area(TSA) of the sphere $=4\pi r^2$
Given, Volume : TSA = 8 : 1
$\therefore \frac{\frac{4}{3}\pi r^3}{4\pi r^2}=\frac{8}{1}$
$\Rightarrow \frac{r}{3}=8$
$\Rightarrow r=24$ units

Hence, the radius of the given sphere is 24 units.