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Question

If a sphere, a cone and a cylinder have the same heights and same radii, then the ratio of their volumes is equal to

A
4 : 2 : 5
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B
2 : 1 : 4
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C
3 : 2 : 4
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D
2 : 1 : 3
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Solution

The correct option is D 2 : 1 : 3
Let the radii of a sphere, a cone and a cylinder be r and their heights be h.

h=2r …..(i)


Volume of sphere =43πr3
Volume of cone =13πr2h
=13πr2×2r [From (i)]
=23πr3
Volume of cylinder =πr2h
=πr2×2r
=2πr3
∴ Ratio of their volumes
= Volume of sphere : Volume of cone : Volume of cylinder
=43πr3:23πr3:2πr3
=23:13:1
= 2:1:3
Hence, the correct answer is option (d).

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