If by melting a solid hemisphere be made into a sphere, then what will be the ratio of their radii?

Explanation

Let the radii of the hemisphere and the sphere be `r_(1)` unit and r_(2) uint respectively. ltbgt So, the volume of the hemisphere =`(2)/(3)pi_(1)^(3)` cubic.unit and the volume of the original sphere`(4)/(3)pir_(2)^(3)` cu.unit.
As per question, `(2)/(3)pir_(1)^(3)=(4)/(3)pir_(2)^(3) "or," r_(1)^(3)/r_(1)^(3)=(4)/(2)=2 "or," (r_(1)/r_(2))^(3)=2 or, r_(1)/(r_(2))=root(3)(2)`
`thereforer_(1):r_(2)=root(3)(2):1`
Hence the required ratio =`root(3)(2):1`