If you have ever SEEN a can of soda, you know what a cylinder looks LIKE. A cylinder is a solid figure with two parallel circles of the same size at the top and bottom. The top and bottom of a cylinder are called the bases. The height

H

of a cylinder is the distance between the two bases. For all the cylinders we will work with here, the sides and the height,

h

, will be perpendicular to the bases.

A cylinder has two circular bases of equal size. The height is the distance between the bases.

An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.

Rectangular solids and cylinders are somewhat similar because they both have two bases and a height. The formula for the volume of a rectangular solid,

V

=

B

h

, can also be used to find the volume of a cylinder.

For the rectangular solid, the area of the base,

B

, is the area of the rectangular base, length × width. For a cylinder, the area of the base,

B

, is the area of its circular base,

π

r

2

. The image below compares how the formula

V

=

B

h

is used for rectangular solids and cylinders.

Seeing how a cylinder is similar to a rectangular solid may make it easier to understand the formula for the volume of a cylinder.

In (a), a rectangular solid is shown. The sides are labeled L, W, and H. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses lw times h, then V equals lwh. In (b), a cylinder is shown. The radius of the top is labeled r, the height is labeled h. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses pi r squared times h, then V equals pi times r squared times h.