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Mathematics

The volume of a solid cylinder and a solid cone are same. If their radii are also same, the ratio between the heights of cylinder and cone is :

  1. 3 : 1

  2. 2 : 3

  3. 1 : 3

  4. 3 : 2

Mensuration

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Answer

Radii of cylinder = Radii of cone = r (let)

Let height of cylinder be h1 and height of cone be h2.

Given,

Volume of a solid cylinder and a solid cone are same.

⇒ πr2h1 = 13\dfrac{1}{3} πr2h2

⇒ h1 = 13\dfrac{1}{3} h2

⇒ h1h2=13\dfrac{h1}{h2} = \dfrac{1}{3}

⇒ h1 : h2 = 1 : 3.

Hence, Option 3 is the correct option.

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