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?
Solution:
Let v1 and v2 be the volumes of the first and second sphere respectively
Radius of the first sphere = r
Radius of the second sphere = 2r
Therefore, $\frac{\text { Volume of first sphere }}{\text { Volume of second sphere }}=\frac{\frac{4}{3} \pi r^{3}}{\frac{4}{3} \pi(2 r)^{3}}$
= 1/8