Lasav of prisms and cylindersupdated

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Lasav of prisms and cylindersupdated

  1. 1. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersWarm UpFind the perimeter and area ofeach polygon.1. a rectangle with base 14 cm and height9 cm2. a right triangle with 9 cm and 12 cmlegs3. an equilateral triangle with side length6 cmP = 46 cm; A = 126 cm2P = 36 cm; A = 54 cm2
  2. 2. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersLearn and apply the formula for thesurface area of a prism.Learn and apply the formula for thesurface area of a cylinder.Objectives
  3. 3. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersExample 3: Finding Surface Areas of CompositeThree-Dimensional FiguresFind the surface area of the composite figure.
  4. 4. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersExample 3 ContinuedTwo copies of the rectangular prism base areremoved. The area of the base is B = 2(4) = 8 cm2.The surface area of the rectangular prism is..A right triangular prism is added to therectangular prism. The surface area of thetriangular prism is
  5. 5. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersThe surface area of the composite figure is the sumof the areas of all surfaces on the exterior of thefigure.Example 3 ContinuedS = (rectangular prism surface area) + (triangularprism surface area) – 2(rectangular prism base area)S = 52 + 36 – 2(8) = 72 cm2
  6. 6. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersCheck It Out! Example 3Find the surface area of the composite figure.Round to the nearest tenth.
  7. 7. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersCheck It Out! Example 3 ContinuedFind the surface area of the composite figure.Round to the nearest tenth.The surface area of the rectangular prism isS =Ph + 2B = 26(5) + 2(36) = 202 cm2.The surface area of the cylinder isS =Ph + 2B = 2(2)(3) + 2(2)2 = 20 ≈ 62.8 cm2.The surface area of the composite figure is the sumof the areas of all surfaces on the exterior of thefigure.
  8. 8. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersS = (rectangular surface area) +(cylinder surface area) – 2(cylinder base area)S = 202 + 62.8 — 2()(22) = 239.7 cm2Check It Out! Example 3 ContinuedFind the surface area of the composite figure.Round to the nearest tenth.
  9. 9. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersAlways round at the last step of the problem. Usethe value of  given by the  key on yourcalculator.Remember!
  10. 10. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersExample 4: Exploring Effects of Changing DimensionsThe edge length of the cube is tripled. Describethe effect on the surface area.
  11. 11. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersExample 4 Continuedoriginal dimensions: edge length tripled:Notice than 3456 = 9(384). If the length, width, andheight are tripled, the surface area is multiplied by 32,or 9.S = 6ℓ2= 6(8)2 = 384 cm2S = 6ℓ2= 6(24)2 = 3456 cm224 cm
  12. 12. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersCheck It Out! Example 4The height and diameter of the cylinder aremultiplied by . Describe the effect on thesurface area.
  13. 13. Holt McDougal Geometry10-4 Surface Area of Prisms and Cylindersoriginal dimensions: height and diameter halved:S = 2(112) + 2(11)(14)= 550 cm2S = 2(5.52) + 2(5.5)(7)= 137.5 cm211 cm7 cmCheck It Out! Example 4 ContinuedNotice than 550 = 4(137.5). If the dimensions arehalved, the surface area is multiplied by
  14. 14. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersExample 5: Recreation ApplicationA sporting goods company sells tents in twostyles, shown below. The sides and floor of eachtent are made of nylon.Which tent requires less nylon to manufacture?
  15. 15. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersExample 5 ContinuedPup tent:Tunnel tent:The tunnel tent requires less nylon.
  16. 16. Holt McDougal Geometry10-4 Surface Area of Prisms and CylindersCheck It Out! Example 5A piece of ice shaped like a 5 cm by 5 cm by 1 cmrectangular prism has approximately the samevolume as the pieces below. Compare the surfaceareas. Which will melt faster?The 5 cm by 5 cm by 1 cm prism has a surface area of70 cm2, which is greater than the 2 cm by 3 cm by4 cm prism and about the same as the half cylinder. Itwill melt at about the same rate as the half cylinder.

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