Question

A solid metal cylinder of base radius 15 centimetres and height 32 centimetres is melted down and recast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

Answer 1

Base radius (r₁) of the solid metal cylinder = 15 cm

Height (h₁) of the solid metal cylinder = 32 cm

Area of base of the solid metal cylinder = πr₁²

= π(15)² cm²

= 225π cm²

Volume of the solid metal cylinder = Area of base × Height

= (225π × 32) cm³

= 7200π cm³

Base radius (r₂) of the new cylinder = 20 cm

Let the height of the new cylinder be h₂ cm.

Base area of the new cylinder = πr₂²

= π(20)² cm²

= 400π cm²

Volume of the new cylinder = (400π × h₂) cm³

= 400πh₂ cm³

Now, volume of the solid metal cylinder = Volume of the new cylinder

⇒ 7200π = 400πh₂

⇒ h₂ =

Therefore, the height of the new cylinder is 18 cm.