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Surface Areas of Prisms & Cylinders Section 11-2

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Objectives To find the surface area of a prism To find the surface area of a cylinder

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All About Prisms Prism - a polyhedron w/ exactly 2 congruent, parallel faces, called bases. Lateral faces - the faces that are not bases in a polyhedron Named by the shape of its bases Altitude - perpendicular segment that joins the planes of the bases Height (h) - length of the altitude

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Vocab Ctd. Lateral area - the sum of the areas of the lateral faces Surface area - the sum of the lateral area and area of the two bases

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Use a net to find the surface area of the cube. Draw a net for the cube. Find the area of one face.11 2 = 121 The area of each face is 121 in. 2. Surface Area = sum of areas of lateral faces + area of bases = ( ) + ( ) = = 726 Because there are six identical faces, the surface area is 726 in. 2.

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You try Use a net to find the S.A. of the triangular prism

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Formulas

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Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number. Use the formula L.A. = ph to find the lateral area and the formula S.A. = L.A. + 2B to find the surface area of the prism. The area B of the base is ap, where a is the apothem and p is the perimeter Draw the base. Use 30°-60°-90° triangles to find the apothem. The triangle has sides of length 18 cm, so p = 3 18 cm, or 54 cm.

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9 = 3 alonger leg 3 shorter leg B = ap = 3 3 54 = The area of each base of the prism is 81 3 cm 2. (continued) S.A. = L.A. + 2BUse the formula for surface area. = ph + 2B = (54)(10) + 2(81 3 )Substitute = Use a calculator. Rounded to the nearest whole number, the surface area is 821 cm a = = = 3 3Rationalize the denominator.

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You try Use formulas to find L.A. & S.A. of the prism

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All About Cylinders Has 2 congruent parallel bases, which are circles. Altitude - perpendicular segment that joins the planes of the bases Height - length of the altitude L.A. - area of resulting rectangle that can be formed by unrolling the cylinder S.A. - sum of the lateral area & area of bases

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The radius of the base of a cylinder is 6 ft, and its height is 9 ft. Find its surface area in terms of. S.A. = L.A. + 2BUse the formula for surface area of a cylinder. = 2 rh + 2( r 2 )Substitute the formula for lateral area of a cylinder and area of a circle. = 2 (6)(9) + 2 (6 2 )Substitute 6 for r and 9 for h. = Simplify. = 180 The surface area of the cylinder is 180 ft 2.

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You try Find the S.A. of a cylinder with a height of 10cm and radius of 10cm in terms of pi. 400cm 2

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A company sells cornmeal and barley in cylindrical containers. The diameter of the base of the 6-in. high cornmeal container is 4 in. The diameter of the base of the 4-in. high barley container is 6 in. Which container has the greater surface area? Find the surface area of each container. Remember that r =. d2d2 S.A. = L.A. + 2B Cornmeal ContainerBarley Container Use the formula for surface area of a cylinder. = 2 rh + 2 r 2 Substitute the formulas for lateral area of a cylinder and area of a circle.

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S.A. = L.A. + 2B Cornmeal ContainerBarley Container Use the formula for surface area of a cylinder. = 2 rh + 2 r 2 Substitute the formulas for lateral area of a cylinder and area of a circle. = 2 (2)(6) + 2 (2 2 ) = 2 (3)(4) + 2 (3 2 ) Substitute for r and h. = = Simplify. = 32 = 42 Because 42 in. 2 32 in. 2, the barley container has the greater surface area. (continued)

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