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Use a net to find the surface area of the cube.

Draw a net for the cube. Surface Area = sum of areas of lateral faces + area of bases. = (121 + 121 + 121 + 121) + (121 + 121). Surface Areas of Prisms and Cylinders. LESSON 11-2. Additional Examples. Quick Check. Use a net to find the surface area of the cube.

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Use a net to find the surface area of the cube.

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  1. Draw a net for the cube. Surface Area = sum of areas of lateral faces + area of bases = (121 + 121 + 121 + 121) + (121 + 121) Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Quick Check Use a net to find the surface area of the cube. Find the area of one face. 112= 121 The area of each face is 121 in.2. = 6 • 121 = 726 Because there are six identical faces, the surface area is 726 in.2.

  2. 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. 1 2 Draw the base. Use 30°-60°-90° triangles to find the apothem. Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number. The triangle has sides of length 18 cm, so p = 3 • 18 cm, or 54 cm.

  3. 9 = 3 alonger leg  3  shorter leg 9 3 3 3 3 a== = 33Rationalize the denominator. 3354 = 1 2 1 2 81 3 B=ap = The area of each base of the prism is 81 3 cm2. S.A. =L.A. + 2BUse the formula for surface area. = 540 + 162 3 =ph + 2B Use a calculator. 2(81 3 ) Substitute = (54)(10) + 9 3 Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Quick Check (continued) Rounded to the nearest whole number, the surface area is 821 cm2.

  4. 2( r2) =2rh + Substitute the formula for lateral area of a cylinder and area of a circle. = 2 (6)(9) + 2 (62) Substitute 6 for r and 9 for h. = 108 + Simplify. = 180 The surface area of the cylinder is 180 ft2. 72 Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples 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. Quick Check

  5. Cornmeal Container Barley Container S.A. =L.A. + 2B Use the formula for surface area of a cylinder. S.A. =L.A. + 2B Substitute the formulas for lateral area of a cylinder and area of a circle. =2rh + 2 r 2 =2rh + 2 r 2 d 2 Find the surface area of each container. Remember that r= . Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples 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?

  6. Substitute for r and h. = (2)(6) + (22) = (3)(4) + (32) 2 2 2 2 Simplify. = 24 + = 24 + 8 = 32 = 42 Because 42 in.2 32 in.2, the barley container has the greater surface area. 18 Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples (continued) Cornmeal Container Barley Container Quick Check

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