if h,c,v are respectively the height, the curved surface area and the volume of a cone, prove that
3πh³-c²h²+9v²=0
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Given, r,h,l,C,V are radius, height, slant height, curved surface and volume of cone, respectively.
We know, volume of the cone V=31πr2h
and curved surface C=πrl=πrh2+r2
Then, 3πVh3−C2h2+9V2
⟹ 3π (31πr2h) h3− (πrh2+r2)h2+9 (31πr2h)2
⟹ π2r2h4 −π2r2h4 −π2r2h4 +π2r2h4 =0.
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