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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 : 3Let 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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