Question:
A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
Solution:
Given that
Volume of the cone = Volume of the hemisphere
$1 / 3 \pi r^{2} h=2 / 3 \pi r^{3}$
$r^{2} h=2 r^{3}$
h = 2r
h/r = 1/1 × 2 = 2
Therefore
Ratio of their heights = 2:1