Question

A spherical shell of lead, whose external and internal diameters are 24 cm and 18 cm, is melted and recast into a right circular cylinder 37 cm high. Find the diameter of the base of the cylinder.

Answer 1

External diameter of the shell = 24 cm
External radius of the shell = 12 cm
Internal diameter of the shell = 18 cm
Internal radius of the shell = 9 cm

Volume of the

`"shell" = 4/3pi (12^3 -9^3) =4/3pi(1728 - 729)=4/3pixx(999)=4pi xx (333) "cm"^3`

Height of cylinder = 37 cm

Let radius of cylinder be r cm.

Volume of cylinder =`pir^2h = 37pir^2  "cm"^3` 

Volume of the shell = Volume of cylinder 

Or, 4π ×(333)= 37πr² 

`⇒ r^2=(4xx333)/37 = 4xx9`

`rArr r =sqrt(4xx9)=sqrt(36) = 6  "cm"`

So, diameter of the base of the cylinder = 2r = 12 cm.