A cylinder has a height h that is 2 times as large as its radius r. Find its volume v.

To find the volume of a cylinder, we use the formula:

V = πr²h

In this problem, we know that the height (h) is 2 times the radius (r), which can be expressed as:

h = 2r

Substituting this into the volume formula gives us:

V = πr²(2r)

Now, simplifying this expression:

V = 2πr³

This formula tells us that the volume of the cylinder, when its height is twice its radius, is equal to 2πr³. Therefore, if you know the radius of the cylinder, you can easily calculate its volume.