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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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Lateral Surface Area Lateral Surface Area is the surface area of the solid’s lateral faces without the base(s).

Lateral Surface Area Lateral Surface Area is the surface area of the solid’s lateral faces without the base(s).

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