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Volume MCQ 2 (Cone, cylinder, volume)

Volume MCQ 2: A right 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_________?

A. 3: 5                 b) 2: 5                c) 3: 1                    d) 1: 3

Solution:

Let ‘r’ be the radius of both, the cylinder of height (suppose h1) and the cone of height (suppose h2)

Right Cylinder

A right cylinder  has top and base vertically upon each other — otherwise it can be a oblique cylinder or any other type depending upon the orientation of base and the top.

According to the figure;

drawit diagram 2

 

Radius of the cylinder = r

Height =h

Use volume formula for a cylinder;

\[ Cylinder Volume=Base Area\times height=\pi r^2\times h \]

or

\[ Cylinder Volume=\pi r^2h \]

Right Cone

A cone in which apex point is vertically above center of the circular base.

drawit diagram 4

According to figure;

Radius of the base of the cone =r

Height from base to apex point =H

Using Volume for mula for a cone;

\[ Cone Volume = \pi r^2 \frac{H}{3} \]

 

We have been given that volumes of both , the cylinder and the cone  – are equal i-e;

 

\[ \pi r^2 h=\pi r^2 \frac{H}{3} \]

Cancelling common terms, we get,

\[ h=\frac {H}{3} \]

or

\[ \frac{h}{H}=\frac{1}{3} \]

 

so the ratio b/w heights is 1:3

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