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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.

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