Question

A hemisphere, a cylinder and a cone have equal base diameters and have the same height .
prove that their volumes are in the ratio 2:3:1
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Answer 1

Volume of cone = (1/3)πr^2h
Volume of hemisphere = (2/3)πr^3
Volume of cylinder = πr^2h
Given that cone, hemisphere and cylinder have equal base and same height
That is r = h
Volume of cone : Volume of hemisphere : Volume of cylinder = (1/3)πr^2h : (2/3)πr^3 : πr^2h
= (1/3)πr^3 : (2/3)πr^3 : πr^3
= (1/3) : (2/3) : 1
= 1: 2: 3