A prism shaped solid whose bases are circles is a **cylinder**. If the segment joining the centers of the circles of a cylinder is perpendicular to the planes of the bases, the cylinder is a **right circular cylinder**. In Figure 1

Figure 1Different types of circular cylinders.

Lateral area, total area, and volume for right circular cylinders are found in the same way as they are for right prisms.

If a cylinder is pictured as a soup can, its lateral area is the area of the label. If the label is carefully peeled off, the label becomes a rectangle, as shown in Figure 2

Figure 2The lateral area of a cylinder.

The area of the label is the area of a rectangle with a height the same as the altitude of the can and a base the same as the circumference of the lid of the can.

*Theorem 90:* The lateral area, *LA*, of a right circular cylinder with a base circumference *C* and an altitude *h* is given by the following equation.

*Theorem 91:* The total area, *TA*, of a right circular cylinder with lateral area *LA* and a base area *B* is given by the following equation.

*Theorem 92:* The volume of a right circular cylinder, *V*, with a base area *B* and altitude *h* is given by the following equation.

**Example 1:** Figure 3 *LA* (b) *TA* and (c) *V*.

**Figure 3** Finding the lateral area, total area, and volume of a right circular cylinder.