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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.

How to find the volume of a cylinder

Although a cylinder is technically not a prism, it shares many of the properties of a prism. Like prisms, the volume is found by multiplying the area of one end of the cylinder (base) by its height.

Since the end (base) of a cylinder is a circle, the area of that circle is given by

Multiplying by the height h we get

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

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.

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. What they usually mean when they say this is the volume enclosed by the cylinder.

Oblique cylinders

Recall that an is one that 'leans over' - where the top center is not over the base center point. In the figure above check "allow oblique' and drag the top orange dot sideways to see an oblique cylinder.

It turns out that the volume formula works just the same for these. You must however use the perpendicular height in the formula. This is the vertical line to left in the figure above. To illustrate this, check 'Freeze height'. As you drag the top of the cylinder left and right, watch the volume calculation and note that the volume never changes.

See Oblique Cylinders for a deeper discussion on why this is so.

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.

Things to try

  1. In the figure above, click 'reset' and 'hide details'
  2. Drag the two dots to alter the size and shape of the cylinder
  3. Calculate the volume of that cylinder
  4. Click 'show details' to check your answer.

Related topics

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