Question

The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.

Answer 1

Inner radius of hollow cylinder r₁ = 15 cm

Outer radius of hollow cylinder r₂ = 20 cm

The volume of hollow cylinder `= pi (r_2^2 - r_1^2) h`

Since,

The hollow cylinder is melted and recast into a solid cylinder of same height.

Let r be the radius of solid cylinder.

Therefore,

The volume of solid cylinder = volume of hollow cylinder.

`pir^2 h = pi (r_2^2 - r_1^2) h`

     `r^2 = (20^2 - 15^2)`

     `r^2 = 35 xx 5`

       `r = 13.2 cm`

Hence, the radius of solid cylinder is13.2 cm .