Question

A metallic solid sphere of radius 10.5 cm is melted and recasted into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made?

Answer 1

Let the number of cones formed be n.

Radius of sphere, r = 10.5 cm

Volume of sphere, `V_1 = 4/3pir^3`

`=>V_1 = 4/3pi(10.5)^3 "cm"^3`

Height of cone, h = 3 cm and radius of cone, R = 3.5 cm

∴ Volume of each smaller cone, `V2 = 1/3pir^2h`

`=> V_2 = 1/3 pi (3.5)^2 xx 3 "cm"^3`

It is given that the solid sphere is melted and recast into smaller cones.

So, n × Volume of each smaller cone = Volume of the sphere

`:. n xx 1/3 pi (3.5)^2 xx 3 = 4/3 pi(10.5)^3`

`=> n = (4 xx (10.5)^3)/((3.5)^2 xx 3)`

`=> n = 126`

Thus, the number of smaller cones formed is 126