Question:
If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?
Solution:
Given that,
A cone and a sphere have equal radii and equal volume
i.e., volume of cone = volume of sphere
$r^{2} h=4 r^{3}$
$h=4 r$
$h=(2 r) \times 2$
$\frac{h}{2 r}=\frac{2}{1}$
$\frac{h}{2}=\frac{2}{1} \quad($ diameterd $=2 r)$
$h: d=2: 1$ or $d: h=1: 2$
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