1. Surface Area of Cylinders

2. Review
8 cm
C = 2πr
A = π r2 15

3. Find the circumference of each circle. Use 3.14 for .
A with a 5 inch radius.
B with a diameter of 41 cm.
Find the area of each circle. Use 3.14 for .

4. SA = 2πrh + 2πr2
Use 3.14 for π. 4

5. SA = 2 π r h + 2 π r2 SA = 2 π (3)(8) + 2 π (3)2
Find the surface area of the cylinder.
SA = 2 π r h π r2
SA = 2 π (3)(8) π (3)2

6. Find the surface area
5 cm
10 cm
3 cm
6 cm
8 ft
15 ft

7. Find the surface area 15-foot tall cylinder with an 8-foot radius.
Find the surface area of a cylinder with a 3 cm radius. The cylinder is 6 cm tall.
3 ft
8 ft 7

8. Example 2a The label on a soup can has a lateral area of approximately
395.6 square centimeters. The height of the can is 9
centimeters. Find the radius of the base of the can.
Use the lateral area formula for a cylinder.
LA = 2πrh
Substitute known values = 2(3.14)r(9)
Multiply = 56.52r
Divide = r
The radius of the base of the soup can is about 7 cm.

9. Example 2b The label on a soup can has a lateral area of approximately
395.6 square centimeters. The height of the can is 9
centimeters. How many square centimeters of aluminum are
needed for the surface area of the entire can?
Use the formula for surface area of a cylinder SA = 2πrh + 2πr2
Substitute known values. SA ≈ 2(3.14)(7)(9) + 2(3.14)(7)2
Multiply, then add SA ≈ ≈
The can needs about cm2 of aluminum.

10. Communication Prompt
How are the formulas for the surface area of a prism and surface area of a cylinder similar?
Describe how to find the total surface area of any cylinder.

13. Lateral Surface Area of a Cylinder
The lateral area (LA) of a cylinder is equal
to the circumference (C) of the base times
the height (h) of the cylinder.
LA = Ch = 2πrh

14. Total Surface Area of a Cylinder
The surface area of a cylinder is equal to the sum of the lateral area (LA) and the area of the two bases.
SA = LA + 2B
SA = 2πrh + 2πr2

15. Example 1 Find the surface area of the cylinder. Use 3.14 for π.
Use the surface area formula.
SA = 2πrh + 2πr2
Substitute all values. SA ≈ 2(3.14)(3)(8) + 2(3.14)(3)2
Multiply, then add. SA ≈ ≈
The surface area of the cylinder is about square inches.