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Q.
Radius and diameter of a sphere are, respectively, equal to the base radius and height of a cone. Find the ratio of their volumes.
Mensuration
Solution:
Let the radius of the sphere be $r \mathrm{~cm}$.
$\therefore \text { Diameter }=2 \mathrm{rcm}$
Base radius of the cone $=r \mathrm{~cm}$
Height $=2 r \mathrm{~cm}$ (given)
$\therefore \text { Required ratio } =\frac{\frac{4}{3} \pi r^3}{\frac{1}{3} \pi r^2(2 r)} (\therefore h=2 r) $
$ =\frac{4}{2}=2: 1$