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Question
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
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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