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Surface Area of Prisms and Cylinders. 10-4. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. Holt Geometry. Warm Up Find the perimeter and area of each polygon. 1. a rectangle with base 14 cm and height 9 cm 2. a right triangle with 9 cm and 12 cm legs

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10-4

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  1. Surface Area of Prisms and Cylinders 10-4 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

  2. Warm Up Find the perimeter and area of each polygon. 1.a rectangle with base 14 cm and height 9 cm 2. a right triangle with 9 cm and 12 cm legs 3. an equilateral triangle with side length 6 cm P = 46 cm; A = 126 cm2 P = 36 cm; A = 54 cm2

  3. Objectives Learn and apply the formula for the surface area of a prism. Learn and apply the formula for the surface area of a cylinder.

  4. Vocabulary lateral face lateral edge prism altitude surface area lateral surface right cylinder

  5. The net of a right prism can be drawn so that the lateral faces form a rectangle with the same height as the prism. The base of the rectangle is equal to the perimeter of the base of the prism.

  6. The surface area of a right rectangular prism with length ℓ, width w, and height h can be written as S = 2ℓw + 2wh + 2ℓh.

  7. Find the lateral area and surface area of the right rectangular prism. Round to the nearest tenth, if necessary.

  8. Find the lateral area and surface area of the right cylinder. Give your answers in terms of .

  9. Example 2B: Finding Lateral Areas and Surface Areas of Right Cylinders Find the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of . Step 1 Use the circumference to find the radius. Circumference of a circle C = 2r Substitute 24 for C. 24 = 2r Divide both sides by 2. r = 12

  10. Example 2B Continued Find the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of . Step 2 Use the radius to find the lateral area and surface area. The height is half the radius, or 6 cm. L = 2rh = 2(12)(6) = 144 cm2 Lateral area S = L + 2r2 = 144 + 2(12)2 = 432 in2 Surface area

  11. Check It Out! Example 2 Find the lateral area and surface area of a cylinder with a base area of 49and a height that is 2 times the radius. Step 1 Use the circumference to find the radius. A = r2 Area of a circle 49 = r2 Substitute 49 for A. Divide both sides by  and take the square root. r = 7

  12. Check It Out! Example 2 Continued Find the lateral area and surface area of a cylinder with a base area of 49and a height that is 2 times the radius. Step 2 Use the radius to find the lateral area and surface area. The height is twice the radius, or 14 cm. Lateral area L = 2rh = 2(7)(14)=196in2 Surface area S = L + 2r2 = 196 + 2(7)2 =294 in2

  13. Example 3: Finding Surface Areas of Composite Three-Dimensional Figures Find the surface area of the composite figure.

  14. A right triangular prism is added to the rectangular prism. The surface area of the triangular prism is Example 3 Continued The surface area of the rectangular prism is . . Two copies of the rectangular prism base are removed. The area of the base is B = 2(4) = 8 cm2.

  15. Example 3 Continued The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure. S = (rectangular prism surface area) + (triangular prism surface area) – 2(rectangular prism base area) S = 52 + 36 – 2(8) = 72 cm2

  16. Find the surface area of the composite figure. Round to the nearest tenth.

  17. Check It Out! Example 3 Continued Find the surface area of the composite figure. Round to the nearest tenth. The surface area of the rectangular prism is S =Ph + 2B = 26(5) + 2(36) = 202 cm2. The surface area of the cylinder is S =Ph + 2B = 2(2)(3) + 2(2)2 = 20 ≈ 62.8 cm2. The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure.

  18. Check It Out! Example 3 Continued Find the surface area of the composite figure. Round to the nearest tenth. S = (rectangular surface area) + (cylinder surface area) – 2(cylinder base area) S = 202 + 62.8 — 2()(22) = 239.7 cm2

  19. Remember! Always round at the last step of the problem. Use the value of  given by the  key on your calculator.

  20. Example 4: Exploring Effects of Changing Dimensions The edge length of the cube is tripled. Describe the effect on the surface area.

  21. 24 cm Example 4 Continued original dimensions: edge length tripled: S = 6ℓ2 S = 6ℓ2 = 6(24)2 = 3456 cm2 = 6(8)2 = 384 cm2 Notice than 3456 = 9(384). If the length, width, and height are tripled, the surface area is multiplied by 32, or 9.

  22. Check It Out! Example 4 The height and diameter of the cylinder are multiplied by . Describe the effect on the surface area.

  23. 11 cm 7 cm Notice than 550 = 4(137.5). If the dimensions are halved, the surface area is multiplied by Check It Out! Example 4 Continued original dimensions: height and diameter halved: S = 2(112) + 2(11)(14) S = 2(5.52) + 2(5.5)(7) = 550 cm2 = 137.5 cm2

  24. Example 5: Recreation Application A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon. Which tent requires less nylon to manufacture?

  25. Example 5 Continued Pup tent: Tunnel tent: The tunnel tent requires less nylon.

  26. Check It Out! Example 5 A piece of ice shaped like a 5 cm by 5 cm by 1 cm rectangular prism has approximately the same volume as the pieces below. Compare the surface areas. Which will melt faster? The 5 cm by 5 cm by 1 cm prism has a surface area of 70 cm2, which is greater than the 2 cm by 3 cm by 4 cm prism and about the same as the half cylinder. It will melt at about the same rate as the half cylinder.

  27. Lesson Quiz: Part I Find the lateral area and the surface area of each figure. Round to the nearest tenth, if necessary. 1. a cube with edge length 10 cm 2. a regular hexagonal prism with height 15 in. and base edge length 8 in. 3. a right cylinder with base area 144 cm2 and a height that is the radius L = 400 cm2 ; S = 600 cm2 L = 720 in2; S 1052.6 in2 L 301.6 cm2; S = 1206.4 cm2

  28. Lesson Quiz: Part II 4. A cube has edge length 12 cm. If the edge length of the cube is doubled, what happens to the surface area? 5. Find the surface area of the composite figure. The surface area is multiplied by 4. S = 3752 m2

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