A cone and a hemisphere have equal bases and equal volumes.
Question:

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Solution:

Given that

A cone and a hemisphere have equal bases and volumes

$V_{\text {cone }}=V_{\text {hemisphere }}$

$1 / 3 \pi r^{2} h=2 / 3 \pi r^{3}$

$r^{2} h=2 r^{3}$

h = 2r

hr = 2/1

h:r = 2:1

Therefore the ratio is 2:1