Question

A cone has one third times the volume of a cylinder with the same base and altitude. True or false?

Answer 1

True(APEX)

A cone has one-third times the volume of a cylinder with the same base and altitude.

Answer 2

Answer:  

The answer is true.

Step-by-step explanation:

Given that the height and base of both cylinder and cone are equal i.e

Let h be the height of cone and cylinder

Let b be the base of cone and cylinder

as both height and base of cone equals to height and base of cylinder.

Now,

$\text{Volume of cylinder=}\pi r^2h$

$\text{Volume of cone=}\pi r^2\frac{h}{3}$

$\frac{\text{volume of cone}}{\text{volume of cylinder}}=\frac{\pi r^2\frac{h}{3}}{\pi r^2h}=\frac{1}{3}$

$\frac{\text{volume of cone}}{\text{volume of cylinder}}=\frac{1}{3}$

$\text{volume of cone}=\frac{1}{3}(\text{volume of cylinder})$

⇒ A cone has one third times the volume of a cylinder with the same base and altitude.

hence, the answer is true.