Question

The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of heigh2`2/3`cm Find the diameter of the cylinder.

Answer 1

Given that,
Internal radius of the sphere = 3cm =`r_1`
External radius of the sphere =5cm=`r_2` 

Height of cylinder=2`2/3cm=8/3cm=h`

Volume of spherical shell = Volume of the cylinder

⇒`4/3π(r_2^3-r_1^3)=πr_3^2h`

⇒ `4/3(5^3-3^3)=8/3r_3^2`

⇒ `(4xx98xx3)/(3xx8)=r_3^2`

⇒ `r_3^2=sqrt(49)`

⇒` r_3= 7cm`

∴ Diameter of the cylinder = 2 (radius) = 14cm.