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Surface Area of Circular Solids Lesson 12.3 cylinder cone sphere

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

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Theorem 113: The lateral area of a cylinder is equal to the product of the height and the circumference of the base. LA cyl = 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. = 2πr 2 + 2πrh

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Find the surface area (total) of the following cylinder: 10cm 7cm TA = 2πr 2 + 2πrh TA = 2π(7 2 ) + 2π(7)(10) TA = 98π + 140π TA = 238π cm 2

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Cone: base is a circle Slant height and lateral height are the same. l Cone will mean a right cone where the altitude passes through the center of the circular base. Net: Theorem 114: The lateral area of a cone is equal to 1 / 2 the product of the slant height and the circumference of the base. LA = ½C l = πr l C = Circumference & l = slant height

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

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Sphere: has NO lateral edges & No lateral area Postulate: TA = 4πr 2 r = radius of the sphere

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Find the total area of the sphere : TA = 4πr 2 = 4π5 2 = 100π units 2

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

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

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