Question

If r₁ and r₂ be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is $\left(r_1^3+r_2^3\right){.}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

Answer 1

Volume of first sphere

Volume of second sphere

Total volume of new sphere

Say of radius of new sphere = r₃

Volume of new sphere

Hence,

So, radius of new sphere