Question

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius R as that of the hemisphere. If H is the height of the cone, then write the values of \[\frac{H}{R} .\]

Answer 1

Given,

Radius of the hemisphere = Radius of the cone.

Now,

Volume of the hemisphere `2/3 piR^3`

and

Volume of the cone `1/3 piR^2 H`

Volume of the hemisphere = volume of the cone

`2/3 piR^2  = 1/3 piR^2 H`

       `2R = H`  or `H/R = 2`