Question

The radius of the base of a right circular cone and the radius of a sphere are each 5 cm in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is ________.

Options

• 5 cm

• 20 cm

• 10 cm

• 4 cm

Answer 1

The radius of the base of a right circular cone and the radius of a sphere are each 5 cm in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is 20 cm.

Explanation:

Let the height of the cone be h.

Volume of cone = `1/3 pir^2h`

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

According to the question,

The volume of cone = Volume of a sphere

`1/3 pir^2h = 4/3pir^3`

∴ h = 4r

h = 4 × 5 cm  ...[∵ Given, r = 5 cm]

∴ h = 20 cm