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A Right Circular Cylinder and a Right Circular Cone Have the Same Radius and the Same Volume. the Ratio of the Height of the Cylinder to that of the Cone is - Mathematics

MCQ

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

Options

  • 3 : 5

  •  2 : 5

  • 3 : 1

  • 1 : 3

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Solution

It is given that the volumes of both the cylinder and the cone are the same.

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 pi r^2h`

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

Volume of cylinder = `pi r^2h`

So we have `(h_"cylinder")/(h_"cone")=(Vpir^2)/(3V pi r^2)`

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

 

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 20 Surface Areas and Volume of A Right Circular Cone
Q 10 | Page 25
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