Question

The diameters of internal and external surfaces of hollow spherical shell are 10cm and 6cm respectively. If it is melted and recast into a solid cylinder of length of 2`2/3`cm, find the
diameter of the cylinder.

Answer 1

Given diameter of internal surfaces of a hollow spherical shell = 10cm

Radius (r)`=10/2=5cm`

External radii (R)`=6/2=3cm`

Volume of a spherica shell (hollow) =`4/3pi(R^2-r^2)`

`V_1=4/3pi(5^2-3^2)cm^3`    ........(1)

Given length of solid cylinder `(h)=8/3`

Let radius of solid cylinder be 'r'

Volume of a cylinder `pir^2h`

`V_2=pir^2(8/3)cm^3`   .........(2)

V₁ = V₂

Equating (1) and (2)

⇒`4/3pi(25-9)=pir^2(8/3)`

⇒`(4/3pi(16))/(pi(8/3))=r^2`

⇒ r² = 49cm

⇒ r = 7cm

d = 2r = 14cm

∴ Diameter of cylinder = 14cm