Question

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Answer 1

Radius (r₁) of hemisphere = 4.2 cm

Radius (r₂) of cylinder = 6 cm

Let the height of the cylinder be h.

The object formed by recasting the hemisphere will be the same in volume.

Volume of sphere = Volume of cylinder

`4/3 pir_1^3 = pir_2^2h`

`4/3pi(4.2)^3 = pi(6)^2h`

`4/3 xx (4.2xx4.2xx4.2)/36 = h`

h = (1.4)³ = 2.74 cm

Hence, the height of the cylinder so formed will be 2.74 cm.