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.

Radius of each cone = 2 cm Height of each cone = 3 cm Radius of sphere = 6 cm

Volume of one cone = (1/3)πr²h

= (1/3)π(2)²(3)

= 4π cm³

Volume of sphere = (4/3)πR³

= (4/3)π(6)³

= 288π cm³

Let the number of cones be n.

Since the cones are melted and recast into the sphere:

n × 4π = 288π

n = 72

Answer:

72 cones.

Melting and recasting do not change the volume of metal. Therefore the total volume of all the cones equals the volume of the sphere.