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Surface Area of Cylinders

Surface Area of Cylinders. Review. C = 2 π r A = π r 2. 8 cm. 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  .

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Surface Area of Cylinders

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  1. Surface Area of Cylinders

  2. Review C = 2πr A = πr2 8 cm 15

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

  4. SA = 2πrh + 2πr2 Use 3.14 for π.

  5. Find the surface area of the cylinder. SA = 2 πr h + 2 πr2 SA = 2 π(3)(8) + 2 π (3)2

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

  7. 8 ft Find the surface area 3 ft 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.

  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. 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.

  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 ≈ 395.64 + 307.72 ≈ 703.36 • The can needs about 703.36 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.

  11. 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

  12. 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

  13. 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.

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