Question

A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius  of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.

Answer 1

Volume of sphere `=4/3 pir^3`…… (i)

Since,

The sphere is recast in to a hollow cylinder of uniform thickness 2 cm.

The external radius of hollow cylinder r₁ = 4 cm

^{The internal radius of hollow cylinder r}₂ ^{= 4 − 2 = 2 cm}

and height, h = 24 cm

Clearly,

The volume of hollow cylinder = volume of sphere

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

`(4^2 - 2^2) xx 24 = 4/3r^3`

             `12 xx 24 = 4/3 r^3`

`r^3 = (12 xx 24 xx 3)/4`

`r= sqrt(12 xx 6 xx 3)`

`=3sqrt (3 xx 2 xx 2 xx 2 xx3 xx 3)`

`r = 6cm`