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Volume enclosed by a cylinder
Definition: The number of cubic units that will exactly fill a cylinder
Try this Drag the orange dot to resize the cylinder. The volume is calculated as you drag.
(If there is no image below, see support page.)

How to find the volume of a cylinder

The volume of a cylinder is found by multiplying the area of one end of the cylinder by its height.
Or as a formula:

where:
π  is Pi, approximately 3.142
r  is the radius of the circular end of the cylinder
h  height of the cylinder

In the figure above, drag the orange dot to resize the cylinder. From the radius and height shown, calculate the volume of the cylinder and verify that it agrees with the calculation in the figure.

Some notes on the volume of a cylinder

Recall that a cylinder is like an empty soup can. It has nothing inside, and the walls of the can have zero thickness. So strictly speaking, the cylinder has zero volume. When we talk about the volume of a cylinder, we really are talking about how much soup it can hold.

Think of it this way: if you took a real, empty metal can and melted it down, you would end up with a small blob of metal. If the can was made of metal with zero thickness, you would get no metal at all. That is what we mean when we say a cylinder has no volume.

The strictly correct way of saying it is "the volume enclosed by a cylinder" - the amount of soup it holds. But many textbooks simply say "the volume of a cylinder" to mean the same thing. However, this is not strictly correct in the mathematical sense. What they usually mean when they say this is the volume enclosed by the cylinder.

Units

Remember that the radius and the height must be in the same units - convert them if necessary. The resulting volume will be in those cubic units. So, for example if the height and radius are both in centimeters, then the volume will be in cubic centimeters.

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(C) 2009 Copyright John Page