Question

A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.

Answer 1

External radius of spherical shell

 `r_1 = 18 /2 = 9 cm`

Let r₂ be the internal radius of spherical shell.

Height of right circular cylinder h = 8 cm

& radius of right circular cylinder

 `r = 12 /2 = 6 cm`

Clearly, volume of spherical shell = volume of right circular cylinder

`4/3 pi (r_1^3 - r_2^3 ) = pi r^2 h`

`4/3(9^3 - r_2^3) = (6)^2 xx 8`

      `729 - r_3^2 =  (36^9 xx 8 xx 3)/4`

`729 - r_2^3 = 216`

` r_2^3 = 513`

` r_2 = 3sqrt513`

` r_2 = 3(19)^(1/3) cm`