If h ,c ,V are respectively the height the curved surface and volume of cone prove that 3πVh^3-C^2h^2+9V^2=0
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Curved surface area of a cone , c = rl
Volume of a cone , V = r2h
L.H.S.= 3Vh3 - c2h2 + 9V2
= 3h3  - (rl)2h2 + 9 
= 2r2h4 - 2r2h2l2 + 9 
= 2r2h4 - 2r2h2(r2 + h2) + 2r4h2 (Since, l2 = r2 + h2)
= 2r2h4 - 2r4h2 - 2r2h4 + 2r4h2 = 0 = R.H.S.
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