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A cylinder is melted in the form of cone, if the radius of the cylinder is equal to the radius of the cone and the height of the cylinder is equal to the square of the height of the cone then find the numerical value of the height of cylinder.

A cylinder is melted in the form of cone, if the radius of the cylinder is equal to the radius of the cone and the height of the cylinder is equal to the square of the height of the cone then find the numerical value of the height of cylinder. Correct Answer 1/3

Given:

The radius of the cylinder = The radius of the cone

The height of the cylinder = Square of the height of the cone

Formula:

Volume of cylinder = πr2h

Volume of the cone = 1/3πr2h

Where, r and h are the radius and height respectively.

Calculation:

[ alt="cylinder to cone" src="//storage.googleapis.com/tb-img/production/21/06/cylinder%20to%20cone.png" style="width: 400px; height: 394px;">

Let the radius of the cylinder and the cone is r.

Let the height of the cone is h.

According to the question,

πr2h2 = 1/3πr2h

⇒ h = 1/3

∴ The numerical value of the height of the cone is 1/3.

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