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Learn to find the surface areas of prisms, pyramids, and cylinders .

Learn to find the surface areas of prisms, pyramids, and cylinders . Vocabulary. surface area net.

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Learn to find the surface areas of prisms, pyramids, and cylinders .

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  1. Learn to find the surface areas of prisms, pyramids, and cylinders.

  2. Vocabulary surface area net

  3. The surface area of a three-dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is the pattern made when the surface of a three-dimensional figure is layed out flat showing each face of the figure.

  4. Additional Example 1A: Finding the Surface Area of a Prism Find the surface area S of the prism. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

  5. Add the areas of each face. Additional Example 1A Continued A: A = 5  2 = 10 B: A = 12  5 = 60 C: A = 12  2 = 24 D: A = 12  5 = 60 E: A = 12  2 = 24 F: A = 5  2 = 10 S = 10 + 60 + 24 + 60 + 24 + 10 = 188 The surface area is 188 in2.

  6. Additional Example 1B: Finding the Surface Area of a Prism Find the surface area S of each prism. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

  7. Additional Example 1B Continued Front: 9  7 = 63 63  2 = 126 Top: 9  5 = 45 45  2 = 90 Side: 7  5 = 35 35  2 = 70 S = 126 + 90 + 70 = 286 Add the areas of each face. The surface area is 286 cm2.

  8. Check It Out: Example 1A Find the surface area S of the prism. Method 1: Use a net. 3 in. A 3 in. 6 in. 3 in. 6 in. 11 in. 6 in. 3 in. 11 in. B D E C 3 in. F Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

  9. Add the areas of each face. Check It Out: Example 1A A: A = 6  3 = 18 3 in. A B: A = 11  6 = 66 3 in. 6 in. 3 in. 6 in. C: A = 11  3 = 33 11 in. D: A = 11  6 = 66 B D E C E: A = 11  3 = 33 3 in. F F: A = 6  3 = 18 S = 18 + 66 + 33 + 66 + 33 + 18 = 234 The surface area is 234 in2.

  10. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces. Check It Out: Example 1B Find the surface area S of each prism. Method 2: Use a three-dimensional drawing. top side front 8 cm 10 cm 6 cm

  11. Check It Out: Example 1B Continued top side front 8 cm 10 cm 6 cm Front: 8  6 = 48 48  2 = 96 Top: 10  6 = 60 60  2 = 120 Side: 10  8 = 80 80  2 = 160 S = 160 + 120 + 96 = 376 Add the areas of each face. The surface area is 376 cm2.

  12. The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

  13. 1 __ S = s2 + 4  ( bh) 2 1 __ Substitute. S = 72 + 4  ( 78)‏ 2 Additional Example 2: Finding the Surface Area of a Pyramid Find the surface area S of the pyramid. S = area of square + 4  (area of triangular face)‏ S = 49 + 4  28 S = 49 + 112 S = 161 The surface area is 161 ft2.

  14. 1 __ S = s2 + 4  ( bh) 2 1 __ S = 52 + 4  ( 510)‏ Substitute. 2 Check It Out: Example 2 Find the surface area S of the pyramid. S = area of square + 4  (area of triangular face)‏ 10 ft 5 ft 5 ft 10 ft S = 25 + 4  25 5 ft S = 25 + 100 S = 125 The surface area is 125 ft2.

  15. Helpful Hint To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface.

  16. Additional Example 3: Finding the Surface Area of a Cylinder Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. ft S = area of curved surface + 2  (area of each base)‏ S = h (2r) + 2  (r2) Substitute. S = 7 (2 4)+ 2  (42)‏

  17. Additional Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = 7  8 + 2  16 S 7  8(3.14) + 2  16(3.14)‏ Use 3.14 for . S 7  25.12 + 2  50.24 S 175.84 + 100.48 S 276.32 The surface area is about 276.32 ft2.

  18. Check It Out: Example 3 Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. 6 ft 9 ft S = area of curved surface + 2  (area of each base)‏ S = h (2r) + 2  (r2) Substitute. S = 9 (2 6)+ 2  (62)‏

  19. Check It Out: Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = 9  12 + 2  36 S 9  12(3.14) + 2  36(3.14)‏ Use 3.14 for . S 9  37.68 + 2  113.04 S 339.12 + 226.08 S 565.2 The surface area is about 565.2 ft2.

  20. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  21. Lesson Quiz Find the surface area of each figure. Use 3.14 for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft2 188.4 ft2 208 ft2

  22. Lesson Quiz for Student Response Systems 1. Find the surface area of a rectangular prism with base length 7 ft, width 6 feet, and height 9 ft. A. 318 ft2 B. 306 ft2 C. 300 ft2 D. 298 ft2

  23. Lesson Quiz for Student Response Systems 2. Find the surface area of a cylinder with radius 5 ft and height 8 ft. Use 3.14 for . A. 576.8 ft2 B. 408.2 ft2 C. 376.2 ft2 D. 251.2 ft2

  24. Lesson Quiz for Student Response Systems 3. Find the surface area of the figure shown. A. 162 ft2 B. 152 ft2 C. 142 ft2 D. 132 ft2

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