Question

# If h,S and V denote respectively the height,curved surface area and volume of a right circular cone,then 3πVh3−S2h2+9V2 is equal to  4 π 32 π2 8 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+h2∴S=πr√r2+h2V=13πr2hNow, 3πVh3−S2h2+9V2=3π(13πr2h)h3−π2r2(r2+h2)h2+9(19π2r4h2)=π2r2h4−π2r4h2−π2r2h4+π2r4h2=0

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