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 height `8/3` cm, find the diameter of the cylinder.

Answer 1

Internal radius of hollow spherical shell = r₁ = 3 cm.
External radius of hollow spherical = r₂ = 5 cm

Volume of hollow spherical = `4/3π(r_2^3 - r_1^3)`
= `4/3π[ (5)^3 - (3)^3]`

= `4/3` π (125 - 127)

= `(4π xx 98)/3`

= `(392π)/3` cm³  

Volume of cylinder = πr²h
= πr² x `8/3`

= `(8 πr^2)/3` cm³ 

Volume of cylinder = Volume of hallow sphere

`(8 πr^2)/3 = (392π)/3`

r² = `(392π xx 3)/(8 π xx 3)`
r² = 49
r = `sqrt49`
r = 7 cm.
The diameter of cylinder = 2r = 2 x 7 = 14 cm.