1. Surface Areas of Cylinders
Find the lateral areas of cylinders.
Find surface areas of cylinders.
Half-pipes are usually in the shape of a cylinder with flat surfaces in the center.

2. LATERAL AREAS OF CYLINDERS
The axis of a cylinder is the segment with endpoints that are centers of its circular bases.
If the axis is also the altitude, then the cylinder is called a right cylinder.
Otherwise, the cylinder is an oblique cylinder.
Base r
Axis
Altitude
Base
Right Cylinder

3. LATERAL AREAS OF CYLINDERS
Base
Base r r
Axis
Axis
Altitude
Altitude
Base
Base
Right Cylinder
Oblique Cylinder

4. Key Concept Lateral Area of a Cylinder
If a right cylinder has a lateral area of L square units, a height of h units, and the bases have radii of r units, then L = 2rh.
2r h

5. Example 1 Lateral Area of a Cylinder
MANUFACTURING An office has recycling barrels for cans and paper. The barrels are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 3 feet tall, and the diameter is 30 inches. How many square feet of cardboard are used to make each barrel?

6. SURFACE AREAS OF CYLINDERS
Find the lateral area and add the area of the bases.

7. Circumference of the bases x height (lateral area)
Key Concept Surface Area of a Cylinder
If a right cylinder has a lateral area of T square units, a height of h units, and the bases have radii of r units, then
T = 2rh + 2r2.
Circumference of the bases x height (lateral area)
Area of the bases r h

8. Example 2 Surface Area of a Cylinder
Find the surface area of the cylinder.
8.3
6.6

9. Example 3 Find the Missing Dimensions
Find the radius of the base of a right cylinder if the surface area is 128 square centimeters and the height is 12 centimeters.
T = 2rh + 2r2
128 = 2r(12) + 2r2 r 12