Question

A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.

Answer 1

Let the number of small cones be 'n'

Volume of sphere

= `4/3pi(8^3 - 6^3)`

= `4/3 xx pi xx 2 xx 148`

Volume of small cones

= `1/3pir^2h`

= `1/3 xx pi xx 2^2 xx 4`

Volume of sphere = n × Volume of small cones

`=> 4/3 xx pi xx 2 xx 148 = n xx 1/3 xx pi xx 2^2 xx 8`

`=> n = (4 xx 2 xx 148 xx 3)/(4 xx 8 xx 3)`

`=>` n = 37

The number of cones = 37 cm.