Question

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

Answer 1

Internal diameter of hollow spherical shell = 6cm

Internal radius of hollow spherical shell =`6/3=3` cm

External diameter of hollow spherical shell = 10 cm 

External radius of hollow spherical shell = `10/2=5`cm

Diameter of cylinder = 14 cm

Radius of cylinder`=14/2=7`cm

Let height of cylinder = xcm

According to the question

Volume of cylinder = Volume of spherical shell

⇒ `pi(7)^2x xx=4/3pi(5^3-3^3)`

⇒`49x xx=4/3(125-27)`

⇒`49x xx=4/3xx98`

`x=(4xx98)/(3xx49)=8/3cm`

∴Height off cylinder=`8/3cm`