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 used.

Answer 1

Let the number of cones melted be n.

Let the radius of sphere be r_s = 6 cm

Radius of cone be r_c = 2 cm

And height of the cone be h = 3 cm

Volume of sphere = n  ...(Volume of a metallic cone)

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

`=> 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.