A solid metal cylinder is of base radius 18 centimetres and height 40 centimetres. By melting this down, how many cylinders of base radius 2 centimetres and height 5 centimetres can be made?

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Solution

Base radius (r₁) of the solid metal cylinder = 18 cm

Height (h₁) of the solid metal cylinder = 40 cm

Base area of the solid metal cylinder = πr₁²

= π(18)² cm²

= 324π cm²

Volume of the solid metal cylinder = Base area × Height

= (324π × 40) cm³

= 12960π cm³

Base radius (r₂) of the new cylinder = 2 cm

Height (h₂) of the new cylinder = 5 cm

Base area of the new cylinder = πr₂²

= π(2)² cm²

= 4π cm²

Volume of the new cylinder = (4π × 5) cm³

= 20π cm³

Number of cylinders that can be made =

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