Question

A sphare of a diameter 15.6 cm. is melted and cast into a right circular cone of height 31.2 cm. find the diameter of base of the cone​

Answer 1

Answer:

Diameter of a sphere = 15.6 cm

Step-by-step explanation:

Radius of the sphere = 15.6 / 2 = 7.8 cm

Volume of a sphere = 4/3 πr3

Volume of the sphere = 4/3 x 22/7 x 7.8 x 7.8 x 7.8

Height of the cone = 31.2 cm

Let the radius of the cone be 'r' cm.

Volume of a cone = 1/3 x πr2h

Volume of the cone = 1/3 x 22/7 x r2 x 31.2

Volume of the cone = Volume of the sphere

1/3 x 22/7 x r2 x 31.2 = 4/3 x 22/7 x 7.8 x 7.8 x 7.8

⇒ r2 = (7.8)2

⇒ r = 7.8 cm

Radius of the cone = 7.8 cm

∴ Diameter of the cone = 2 x 7.8 = 15.6 cm