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

Question

asked Sep 16, 2019 200k views

2 Answers

Mircea Voivod · Answer 1 · 2019-09-21T06:29:22+0000

Answer:

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.