Question

Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are metled and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.

Answer 1

For cylinder 1,

Height = h₁ = 30 cm

Radius = r₁ = `60/2` = 30 cm

Volume = V₁

= `pir_1^2h_1`

= π × 30 × 30 × 30

= 27000π cm³

For cylinder 2,

Height = h₂ = 60 cm

Radius = r₂ = 30 cm

Volume = V₂ 

= `pi "r"_2^2 "h"_2`

= π × 30 × 30 × 60

= 54000π cm³

Let r be the radius of the third cylinder.

Height = h = 10 cm

Volume = V

= πr²h

= πr² × 10

Now,

V = V₁ + V₂ 

`=>` πr² × 10 = 27000π + 54000π 

`=>` πr² × 10 = 81000π

`=>` r² = 8100

`=>` r = 90

`=>` Diameter = 2r = 180 cm