Question

How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?

Answer 1

Let the number of cylinders be n.

Radius of a sphere (r) = 30 cm

Radius of the cylinder (R) = 10 cm

Height of the cylinder (H) = 6 cm

∴ Volume of the sphere = `4/3 pir^3`

= `4/3 xx pi(30)^3`

= 4 × π × 10 × (30)²

= 4 × π × 9000

= 36000 π

Volume of cylinder = πR²H

= π × (10)² × 6

= π × 100 × 6

= 600 π

∴ Number of cylinders that can be made by sphere = `("Volume of the sphere")/("Volume of cylinder")`

= `(36000 π)/(600 π)`

= 60

∴ There are 60 cylinders that can be made by using spheres.