The base radius of an iron cylinder is 15 centimetres and its height is 32 centimetres. It is melted and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

Given: radius of old cylinder “r₁” = 15cm

Height of old cylinder “h₁” = 32cm

Radius of new cylinder “r₂” = 20cm

∏ = 3.14

To find : height of the new cylinder “h₂” = ?

Procedure :

As we know that the new cylinder id formed by melting the old cylinder.

∴ volume of old cylinder = volume of new cylinder

Now, volume of old cylinder = Base area of old cylinder × height of old cylinder

⇒ volume of old cylinder = ∏×(r₁)² × h₁

= ∏×15²×32

Now, volume of new cylinder = ∏×(r₂)² × h₂

= ∏×(20)² × h₂

As we know, the volumes of the new and old cylinders is same, so we can now equate them.

⇒ volume of old cylinder = volume of new cylinder

⇒ ∏×15²×32 = ∏×(20)² × h₂

⇒ 15²×32 = 20² × h₂

⇒ h₂ =

=

=

= 18cm.

∴ the height of the newly formed cylinder is 18cm.