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Surface Area of Prisms and Cylinders - Warm Up Lesson Presentation

This lesson presentation introduces the concept and formulas for finding the surface area of prisms and cylinders. It includes examples and practice problems for both right and oblique prisms and cylinders.

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Surface Area of Prisms and Cylinders - Warm Up Lesson Presentation

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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 right prism oblique prism altitude surface area lateral surface axis of a cylinder right cylinder oblique cylinder

  5. Parts of a prism!

  6. An altitudeof a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude. Surface areais the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces.

  7. 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.

  8. Prism Formula! The surface area of a right rectangular prism with length ℓ, width w, and height h can be written as S = 2ℓw + 2wh + 2ℓh. FORMULA ON THE STATE ASSESSMENT!!! All other prisms: SA = Ph + 2B P = Perimeter of the base B = Base Area

  9. Caution! The surface area formula is only true for right prisms. To find the surface area of an oblique prism, add the areas of the faces.

  10. Example 1A: Finding Lateral Areas and Surface Areas of Prisms Find the lateral area and surface area of the right rectangular prism. Round to the nearest tenth, if necessary. L = Ph P = 2(9) + 2(7) = 32 ft = 32(14) = 448 ft2 S = Ph + 2B = 448 + 2(7)(9) = 574 ft2

  11. Example 1B: Finding Lateral Areas and Surface Areas of Prisms Find the lateral area and surface area of a right regular triangular prism with height 20 cm and base edges of length 10 cm. Round to the nearest tenth, if necessary. L = Ph = 30(20) = 600 cm2 P = 3(10) = 30 cm S = Ph + 2B The base area is

  12. Warm Up Find the lateral area and surface area of a cube with edge length 8 cm. L = Ph = 32(8) = 256 cm2 P = 4(8) = 32 cm S = Ph + 2B = 256 + 2(8)(8) = 384 cm2

  13. Right and oblique Cylinders!

  14. Cylinder Formula!

  15. Example 2A: Finding Lateral Areas and Surface Areas of Right Cylinders Find the lateral area and surface area of the right cylinder. Give your answers in terms of . The radius is half the diameter, or 8 in. L = 2rh = 2(8)(10) = 160 in2 S = L + 2r2 = 160 + 2(8)2 = 288 in2

  16. 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

  17. 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

  18. Example 3: Finding Surface Areas of Composite Three-Dimensional Figures Find the surface area of composite figure. Can you see the two shapes?

  19. 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.

  20. 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

  21. Check It Out! Example 3 Find the surface area of the composite figure. Round to the nearest tenth.

  22. 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.

  23. 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

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

  25. Example 4: Exploring Effects of Changing Dimensions CUBE FORMULA! SA = 6s2 Volume = s3 How will the surface area change if the sides are tripled?

  26. 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.

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

  28. 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

  29. 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?

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

  31. Warm Up 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. L = 400 cm2 ; S = 600 cm2 L = 720 in2; S 1052.6 in2

  32. 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

  33. Assignment Page 684 13, 15-22 all

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