Surface Area of Cylinders

Review

C = 2πr

A = π r215

8 cm

Find the circumference of each circle. Use 3.14 for .

11 1A with a 5 inch radius.

11 1B with a diameter of 41 cm.

Find the area of each circle. Use 3.14 for .

11 1A with a 5 inch radius.

11 1B with a diameter of 41 cm.

SA = 2πrh + 2πr2

Use 3.14 for π.

Find the surface area of the cylinder.

SA = 2 π r h + 2 π r2

SA = 2 π (3)(8) + 2 π (3)2

Find the surface area

8 ft

15 ft

3 cm

6 cm

5 cm

10 cm

1. 15-foot tall cylinder with an 8-foot radius.

2. Find the surface area of a cylinder with a 3 cm radius. The cylinder is 6 cm tall.

Find the surface area

3 ft

8 ft

The label on a soup can has a lateral area of approximately395.6 square centimeters. The height of the can is 9centimeters. Find the radius of the base of the can.

Use the lateral area formula for a cylinder. LA = 2πrh

Substitute known values. 395.6 = 2(3.14)r(9) Multiply. 395.6 = 56.52r Divide. 56.52 56.52

7 = r The radius of the base of the soup can is about 7 cm.

The label on a soup can has a lateral area of approximately395.6 square centimeters. The height of the can is 9centimeters. How many square centimeters of aluminum areneeded 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 ≈ 395.64 + 307.72 ≈ 703.36

The can needs about 703.36 cm2 of aluminum.

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.

The lateral area (LA) of a cylinder is equalto the circumference (C) of the base times

the height (h) of the cylinder.

LA = Ch = 2πrh

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

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 ≈150.72 + 56.52 ≈ 207.24

The surface area of the cylinder is about 207.24 square inches.