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