Question

the radìi of base two cone of same geight r1 and r2 respectively.the cone are melted and he cost into a solid sphere of radius and show that height of each cone is h=4Rsquare/rsquare1 + rsquare 2

Answer 1

let r and r2 be the radius of Two right circular cone and let h be its height

let R be the radius of the sphere

$To \: show \: = \frac{4 {R \: }^{3} }{ {r1}^{2} + {r2}^{2} }$
Proof -

Volume of Two cone = Volume of sphere

$\frac{1}{3} \pi \: {r1}^{2} \times h+ \frac{1}{3} \: \times h \: \pi \: {r2}^{2} = \frac{4}{3} \times \pi \times {r}^{3} \\ \\ = ( {r1}^{2} + {r2}^{2} )h = 4 {r}^{3} \\ \\ = h = \frac{4 {R}^{3} }{ {r1}^{2} + {r2}^{2} }$
Hence proved

Hope this helps u !!