Question

4. If the radius of a sphere is doubled then what is the
ratio of their volumes?​

Answer 1

Solution:

Let original radius of the sphere be R.

When radius is doubled it becomes 2R.

$\boxed{\sf{Volume \ of \ sphere =\dfrac{4}{3}\times\pi\times \ r^{3}}} \\ \\ \sf{Ratio=\dfrac{\frac{3}{4}\times\pi\times \ R^{3}}{\frac{3}{4}\times\pi\times(2R)^{4}}} \\ \\ \sf{\therefore{Ratio=\dfrac{R^{3}}{(2R)^{3}}}} \\ \\ \sf{\therefore{Ratio=\dfrac{R^{3}}{8R^{3}}}} \\ \\ \sf{\therefore{Ratio=1:8}}$

The ratio of their volumes is 1 : 8.