Question

If the radius of two spheres are in the ratio $1:3$, find the ratio of their volumes.

Answer 1

The ratio of the radius is $1:3$

Let the common factor be $r$

The volume of the first sphere is $\frac{4}{3}\pi r^3$

The volume of the Second sphere is $\frac{4}{3}\pi (3r{)}^3$$=27\left(\frac{4}{3}\pi r^3\right)$

The ratio is $\frac{4}{3}\pi r^3:27\left(\frac{4}{3}\pi r^3\right)$

$=1:27$