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Q.

The radius and the volume of a right circular cylinder and cone are the same. The ratio of the cylinder's height to the cone's height is


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a

3 : 5

b

2 : 5

c

3 : 1

d

1 : 3  

answer is D.

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Detailed Solution

It is given that the radius and the volume of a right circular cylinder and cone are the same.
We know that the volume of the cone is 1 3 π r 2 h,   where r is the radius of the base and h is the cone's height.
The volume of a cylinder is π r 2 h,    where r is the radius of the base and h is the cylinder's height.
Let the height of a right circular cone and a right circular cylinder be H cm and h cm respectively.
Since a right circular cylinder and a right circular cone has the same radius and the same volume, therefore we have,
    π r 2 h= 1 3 π r 2 H ⇒h= 1 3 H ⇒ h H = 1 3  
Thus, the ratio of the cylinder's height to the cone's height is 1 : 3.
Hence, option (4) is correct.
 
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