Question

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

Answer 1

Let, the height of cone = h and height of hemisphere = H

∴ Volume of cone = Volume of hemisphere

`1/3 πr^2h = 2/3 πr^3`

`1/3 πr^2h = 2/3 πr^2"H`          ...( ∵ H = r )

`h/H = (2πr^2 xx 3)/(3 πr^2)`

`h/H = 2/1`

h: H = 2: 1.