Question

Suppose que le rayon d'un cylindre est indentique à sa hauteur. Qu'arriverait-il au volume de ce cylindre si le rayon était multiplié par deux et si sa hauteur était la moitié

Answer 1

Answer: The volume is doubled.

Explanation:

I will answer in English.

This says that:

"The radius of a cylinder is equal to its height, what would happen to the volume of this cylinder if the radius is doubled, and the height is halved?"

The volume of a cylinder of radius R y height H is:

V = pi*R^2*H

In this case, the radius is equal to the height, then the initial volume is:

V = pi*(R^2)*R = pi*R^3

Now, for the new cylinder we will have:

Radius = 2*R

Height = R/2

Then the new volume is:

V' = pi*(2*R)^2*(R/2)

V' = pi*4*R^2*(R/2)

V' = (4/2)*pi*R^2*R

V' = 2*pi*R^3

And pi*R^3 was the volume of the original cylinder, then:

V' = 2*V

This means that when the radius is doubled and the height is halved, the volume of the cylinder is doubled.