Question

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.

Answer 1

We have,

the internal base radius of spherical shell, r₁ = 3 cm,

the external base radius of spherical shell, r₂ = 5 cm and 

the base radius of solid cylinder , r = 14/2 = 7 "cm".

Let the height of the cylinder be h.

As, 

Volume of solid cylinder = volume of spherical shell 

`rArr pir^2h = 4/3 pir_2^3 - 4/3pir_1^3`

`rArr pir^2h = 4/3pi(r_2^3 - r_1^3)`

`rArr r^2h =4/3 (r_2^3 - r_1^3)`

`rArr 7xx7xxh = 4/3(5^3-3^3)`

`rArr 49xx h =4/3(125-27)`

`rArr h = 4/3xx98/49`

`therefore h = 8/3 "cm"`

So, the height of the cylinder is `8/3` cm.