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