Surface Area of Cylinders

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Lesson 9-3: Cylinders and Cones

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Surface Area of Cylinders

Review 8 cm C = 2πr A = π r2 15

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 .

SA = 2πrh + 2πr2 Use 3.14 for π. 4

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 + 2 π r2 SA = 2 π (3)(8) + 2 π (3)2

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

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

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. 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.

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 ≈ 395.64 + 307.72 ≈ 703.36 The can needs about 703.36 cm2 of aluminum.

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.

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

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

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 ≈150.72 + 56.52 ≈ 207.24 The surface area of the cylinder is about 207.24 square inches.