Question

A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio

Options

• 9 : 1

• 1 : 9

•  3 : 1

• 1 : 3

Answer 1

Since the cylinder is re cast into a cone both their volumes should be equal.

So, let Volume of the cylinder = Volume of the cone

= V

It is also given that their base radii are the same.

So, let Radius of the cylinder = Radius of the cone

= r

Let the height of the cylinder and the cone be h_cylinder and  `h_"cone"` respectively.

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

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

The formula of the volume of a cylinder with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cylinder = `pir^2h`

So we have

`("Volume of cone" )/("Volume of cylinder") = (1/3pir^2h_"cone")/(pir^2h_"cylinder")`

`⇒ V/V =(1/3h_"cone")/(h_"cylinder")`

`⇒1=(1/3h_"cone")/(h_"cylinder")`

`(h_"cone " )/(h_"cylinder") = 3/1`