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Surface Area of Circular Solids Lesson 12.3

Surface Area of Circular Solids Lesson 12.3. cone. cylinder. sphere. Cylinder : Contains 2 congruent parallel bases that are circles. Right circular cylinder perpendicular line from center to each base. Net :. h. r. Theorem 113 :

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Surface Area of Circular Solids Lesson 12.3

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  1. Surface Area of Circular SolidsLesson 12.3 cone cylinder sphere

  2. Cylinder: Contains 2 congruent parallel bases that are circles. Right circular cylinder perpendicular line from center to each base. Net: h r

  3. Theorem 113: The lateral area of a cylinder is equal to the product of the height and the circumference of the base. LAcyl= Ch = 2πrh (C = circumference, h= height) h r The total area of a cylinder is the sum of the cylinder’s lateral area and the areas of the two bases. T.A. = 2πr2 + 2πrh

  4. Find the surface area (total) of the following cylinder: 7cm TA = 2πr2+ 2πrh TA = 2π(72) + 2π(7)(10) TA = 98π + 140π TA = 238π cm2 10cm

  5. Cone: base is a circle Slant height and lateral height are the same. l Net: Cone will mean a right cone where the altitude passes through the center of the circular base. Theorem 114: The lateral area of a cone is equal to1/2 the product of the slant height and the circumference of the base. LA = ½Cl= πrl C = Circumference & l = slant height

  6. The total surface area of a cone is the sum of the lateral area and the area of the base. TA = πr2 + πrl Find the surface area of the cone. The diameter is 6 & the slant height is 8. TA = πr2 + πrl = π(3)2 + π3(8) = 9π + 24π = 33π units2

  7. Sphere:has NO lateral edges & No lateral area Postulate: TA = 4πr2 r = radius of the sphere

  8. Find the total area of the sphere: TA = 4πr2 = 4π52 = 100π units2

  9. As a team, find the surface area of the following shape. Only find the area of the parts you can see. 17cm 16cm 10cm

  10. 1. Lateral area of a cone, πrl =π8(17) = 136π 2. Plus the lateral area of the cylinder, 2πrh = 2π(8)(10) = 160π 3. Plus the surface of the hemisphere. 4πr2 = (1/2)4π(82) = 128π Add them up: 136π + 160π + 128π= 424πunits2

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