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Question

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of cylinder to cone is 4:3, the ratio of their volume is


A

2:1

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B

3:1

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C

4:1

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D

1:1

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Solution

The correct option is C

4:1


Let Radius of the conical dome = Radius of the cylindrical pillar = r

Let the height of the cylindrical pillar and conical dome be hcylinder and hcone respectively.

Given, hcylinder:hcone=4:3

Let hcylinder=4x then hcone=3x

Ratio of their volume =Volume of the cylindrical pillarVolume of the conical dome=πr2hcylinder13πr2hcone

=πr2×413πr2×3

=4:1


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