Question

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.

Answer 1

Let the number of cones be n.

Let the radius of the sphere be r_s = 6 cm

Radius of a cone is r_c = 2 cm

And the height of the cone is h = 3 cm

Since the cones are melted and recast into a sphere, the total volume remains the same.

Therefore, the volume of the sphere = n × the volume of one cone.

`=> 4/3 pir_s^3 = n(1/3 pir_c^2h)`

`=> (4r_s^3)/(r_c^2h) = n`

`=> n = (4(6)^3)/((2)^2(3))`

`=> n = (4 xx 216)/(4 xx 3)`

n = 72

Hence, the number of cones is 72.