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  • A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Direction: Write True or False and justify your answer in each of the following :

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

 

 

Answers (1)

Answer : True

We know that

Volume of cylinder =\pi R^{2}H             (where R is the radius and H is height)

Volume of cone =\frac{1}{3}\pi r^{2}h                 (where r is the radius and h is height)

Given that a cylinder and a right circular cone are having the same base and same height.

So let r be the radius and h be the height of both.

Now, Volume of cylinder will be , V_{1}=\pi r^{2}h

and Volume of cone will be, V_{2}=\frac{1}{3}\pi r^{2}h

So we get:

\therefore V_{2}=\frac{1}{3}V_{1}

Therefore, V_{1}=3V_{2}

Hence, the  statement is true.

Posted by

infoexpert23

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