Question

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

Answer 1

For sphere, radius = R = 15 cm

For cone, radius = r = 2.5 cm, height, h = 8 cm

Let the number of cones recast be n.

∴ n x Volume of one cone = Volume of solid sphere

`=> n xx 1/3 pir^2h`

= `4/3pir^3`

`n × 1/3 ​π(2.5)^2(8) = 4/3π(15)^3`

Now multiply both sides by 3 (this is the “missing” step you’re thinking of):

`=> nπ xx (2.5)^2 xx (8) = 4π xx (15)^3`    ...[Cancel π from both sides]

`=> n = (4 xx 15 xx 15 xx 15)/(2.5 xx 2.5 xx 8)`

`=> n = 270`

Thus, 270 cones were recast.