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Question

If h, S, and V denote respectively the height, curved surface area, and volume of a right circular cone, then 9πVh3S2h29V2 is equal to _____. (Given: r=h)

A

π2r4
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B

π2r6
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C

1
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D

0
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Solution

The correct option is D
0

h = height , S = curved surface area and V = volume of the cone

Let r be the radius of the cone. Then

S=πrl, where l=r2+h2S=πrr2+h2V=13πr2hNow, 9πVh3S2h29V2=9π(13πr2h)h3π2r2(r2+h2)h29(19π2r4h2)=3π2r2h4π2r4h2π2r2h4π2r4h2=0[By substituting r=h]


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