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* = π*rl* and

Slant height of the cone,

3π*Vh*^{3}* – *C^{2}*h*^{2} + 9*V*^{2}

= π^{2} *r*^{2 }*h*^{4 }– π^{2} *r*^{2 }(*r*^{2 }+ *h*^{2}) *h*^{2 }+ π^{2 }*r*^{4 }*h*^{2}

= π^{2} *r*^{2 }*h*^{4 }– π^{2} *r*^{4 }*h*^{2 }– π^{2 }*r*^{2 }*h*^{4 }+ π^{2 }*r*^{4 }*h*^{2}

= 0

Thus, 3π*Vh*^{3} – *C*^{2}*h*^{2 }+ 9*V*^{2} = 0

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