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

The answer is true.

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(h)/(3)`

`\frac{\text{volume of cone}}{\text{volume of cylinder}}=(\pi r^2(h)/(3))/(\pi r^2h)=(1)/(3)`

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

`\text{volume of cone}=(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.