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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 3πVh3S2h2+9V2 is equal to 


  1. 4 π

  2. 32 π2

  3. 8

  4. 0


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, 3πVh3S2h2+9V2=3π(13πr2h)h3π2r2(r2+h2)h2+9(19π2r4h2)=π2r2h4π2r4h2π2r2h4+π2r4h2=0

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