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The radius of the base of a right circular cone and a sphere is each equal. If the volume of sphere and cone is same, then what is the ratio of height of cone to the radius of sphere.

The radius of the base of a right circular cone and a sphere is each equal. If the volume of sphere and cone is same, then what is the ratio of height of cone to the radius of sphere. Correct Answer 4 : 1

Given:

Radius of a cone = Radius of sphere.

Volume of cone = Volume of sphere

Formula Used:

Volume of cone = πr2.h/3

Volume of sphere = 4/3πr3

Calculation:

Let the radius of cone and sphere be r

According to the question,

⇒ πr2.h/3 = 4/3πr3

⇒ h = 4r

⇒ h/r = 4/1

⇒ h : r = 4 : 1

∴ The ratio of height of a cone and radius of a sphere is 4 : 1

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