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The volume of a right circular cone is equal to that of a sphere, whose radius is half the radius of the base of the cone. What is the ratio of the radius of the base to the height of the cone?

The volume of a right circular cone is equal to that of a sphere, whose radius is half the radius of the base of the cone. What is the ratio of the radius of the base to the height of the cone? Correct Answer 2 : 1

Let the radius of the right circular cone be r.

So,

Radius of sphere = r/2

According to the question,

The volume of a right circular cone = volume of a sphere

⇒ 1/3 × π × r12 × h = 4/3 × π × r23

⇒ r2× h = 4 × r3/8

⇒ h/r = ½

Ratio of the radius of the base to the height of the cone = 2 : 1

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