Question

If the radius of the sphere is doubled, Find the ratio of volume of the new sphere to the original sphere.

Answer 1

Dear student

Let the radius of the two spheres be r and 2r.

So the ratio of the volume of the two spheres be
$$\begin{gathered} \frac{\mathrm{Volume}\mathrm{of}\mathrm{new}\mathrm{sphere}}{\mathrm{Volume}\mathrm{of}\mathrm{original}\mathrm{sphere}} \\ =\frac{{\displaystyle \frac{4}{3}}\mathrm{\pi }\left(2{\mathrm{r}}^3\right)}{{\displaystyle \frac{4}{3}}\mathrm{\pi }{\left(\mathrm{r}\right)}^3} \\ =\frac{8}{1} \end{gathered}$$
Regards