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EXAMPLE 1

Find the surface area of the cylinder at the right. Use 3.14 for π. Use a net to find the surface area. ≈. 3.14( 3 ) 2. EXAMPLE 1. Finding the Surface Area of a Cylinder. SOLUTION. METHOD 1. Area of base:. A = π r 2. = 28.26 cm 2. 2(3.14)( 3 )( 8 ). ≈. S.

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EXAMPLE 1

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  1. Find the surface area of the cylinder at the right. Use 3.14 for π. Use a net to find the surface area. ≈ 3.14(3)2 EXAMPLE 1 Finding the Surface Area of a Cylinder SOLUTION METHOD 1 Area of base: A=πr2 = 28.26cm2

  2. 2(3.14)(3)(8) ≈ S = 28.26 + 28.26 + 150.72 2πr2 2πrh + S = 2(3.14)(3)2 + 2(3.14)(3)(8) ≈ EXAMPLE 1 Finding the Surface Area of a Cylinder Area of curved surface: A= 2πrh = 150.72 cm2 Surface area: = 207.24 METHOD 2 Use the formula for the surface area of a cylinder. Write formula for surface area. Substitute values. = 56.52 + 150.72 Multiply. = 207.24 Add.

  3. ANSWER The surface area is about 207 square centimeters. 2(3)(3)2 + 2(3)(3)(8) ≈ EXAMPLE 1 Finding the Surface Area of a Cylinder Check To check that your answer is reasonable, use 3 for π. S Substitute values into formula. = 54 +144 Multiply. = 198 Add. Because 198 is close to 207, a surface area of 207 cm2 is reasonable.

  4. S = 2πr2 2πrh + 244.92 ≈ 2(3.14)(3)2 + 2(3.14)(3)h 244.92 = 56.52 + 18.84h – – 244.92 56.52 = 56.52 + 18.84h 56.52 EXAMPLE 2 Finding the Height of a Cylinder Balance Board The balance board shown on page 649 rocks back and forth on a wooden cylinder. The cylinder has a radius of 3 inches and a surface area of 244.92 square inches. Find the height of the cylinder. Use 3.14 for π. Write formula for surface area. Substitute values. Multiply. Subtract 56.52 from each side.

  5. ANSWER The height of the wooden cylinder is about 10 inches. EXAMPLE 2 Finding the Height of a Cylinder 188.4 = 18.84h Simplify. 10 = h Divide each side by 18.84.

  6. 1. S = 2πr2 2πrh + 2(3.14)(5)2 + 2(3.14)(5)(3) ≈ ANSWER The surface area is about 251.2 mm2. for Example 2 and 3 GUIDED PRACTICE GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 GUIDED PRACTICE Find the surface area of the cylinder. Use 3.14 for π. Write formula for surface area. Substitute values. = 157 + 94.2 Multiply. = 251.2 Add.

  7. 2. S = 2πr2 2πrh + 2(3.14)(4)2 + 2(3.14)(4)(12) ≈ ANSWER The surface area is about 401.92 ft2. for Example 2 and 3 GUIDED PRACTICE GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 GUIDED PRACTICE Write formula for surface area. Substitute values. = 100.48 + 301.44 Multiply. = 401.92 Add.

  8. 3. S = 2πr2 2πrh + Diameter radius = , so r = . 11 11 2 ≈ 2(3.14) + 2(3.14) (12) 2 3 3 11 ANSWER 2 The surface area is about 570 m2. for Example 2 and 3 GUIDED PRACTICE GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 GUIDED PRACTICE Write formula for surface area. = 189.97 + 379.94 Multiply. = 569.91 Add.

  9. S = 2πr2 2πrh + 2(3.14)(20)2 + 2(3.14)(20)(h) 9700 ≈ 7188 125.6h = 125.6 125.6 for Example 2 and 3 GUIDED PRACTICE GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 GUIDED PRACTICE 4. Find the height of a cylinder that has a radius of 20 feet and a surface area of 9700 square feet. Use 3.14 for π. Round your answer to the nearest foot. Write formula for surface area. Substitute values. 9700 = 2512 + 125.6h Multiply. Subtract 2512 fromeach side 9700 – 2512 = 2512 + 125.6h – 2512 7188 = 125.6h Simplify. Divide each side by 125.6

  10. ANSWER The height of the cylinder is about 57ft. GUIDED PRACTICE for Examples 1 and 2 h = 57.23

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