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If h,C,V respectively are the height, th...

If h,C,V respectively are the height, the curved surface area and volume of a cone. Prove that `3pi Vh^(3)-C^(2)h^(2)+9V^(2)=0`.

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`C=pirl,V=(1)/(3)pir^(2)h, l^(2)=h^(2)+r^(2)`
L.H.S=`3piVh^(3)-C^(2)h^(2)+9V^(2)`
`=(3pi)((1)/(3)pir^(2)h)-(pirl)^(2)-(pirl)^(2)h^(2)+9((1)/(3)pir^(2)h)^(2)`
`=pi^(2)r^(2)h^(4)-pi^(2)r^(2)h^(2)(h^(2)+r^(2))+9xx(1)/(9)pi^(2)r^(2)h^(2)`
`pi^(2)r^(2)h^(4)-pi^(2)r^(2)h^(4)-pi^(2)r^(2)h^(4)-pi^(2)r^(4)h^(2)`=0=R.H.S
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