Question

If the radius of a sphere is doubled, then what is the ratio of their volumes?

Answer 1

Let the original radius be r

so the original volume = $\frac{4}{3}\pi r^3$

New radius = 2r

so, new volume = $\frac{4}{3}\pi (2r{)}^3=\frac{4}{3}\pi (8r^3)$

Ratio = $\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi \left(8r^3\right)}=\frac{1}{8}$

so ratio = 1:8