if h,c,v are respectively the height, curved surface area and the volume of a cone.prove that

3 pie v h cube - c2h2 + 9v2 =0

Given h, C, V are the height, curved surface area and volume of the cone respectively.

C = πrl  and  

Slant height of the cone,

Vh3 – C2h2 + 9V2

= π2 r2 h4  –  π2 r2  (r2 + h2) h2 +  π2 r4 h2

= π2 r2 h4  –  π2 r4 h2  –  π2 r2 h4  + π2 r4 h2

= 0

Thus, 3πVh3C2h2 + 9V2 = 0

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