Question

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

Answer 1

Let $r$ be the radius of the given sphere, then volume $=\frac{4}{3}\pi r^3$
By doubling the radius, the radius of the new sphere = 2r
$\therefore Volume=\frac{4}{3}\pi (2r{)}^3=\frac{4}{3}\pi \times 8r^3=8\left(\frac{4}{3}\pi r^3\right)$
$\therefore$ Ratio in their volumes
$=\frac{4}{3}\pi r^3:8\times \frac{4}{3}\pi r^3=1:8$