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Surface Area of Prisms and Cylinders Lesson 9-8

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Vocabulary A net is a pattern you can fold to form a three-dimensional figure. This is a net for a triangular prism.

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The surface area of a three- dimensional figure is the sum of the areas of its surfaces. Find the area of each surface, and add all the areas together.

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Example 1 26 cm 8 cm 18 cm Triangles A = ½ bh A = ½ (26)(18) A = ½ (468) A = 234 cm 2 2 Tri’s: 234 x 2 = 468 cm 2 Left Rectangle A = lw A = (18)(8) A = 144 cm 2 Front and Back Rectangles A = lw A = (26)(8) A = 208 cm 2 2 Rect’s: 208 x 2 = 416 cm 2

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Add up the areas to find surface area. S.A. = 468 cm 2 + 144 cm 2 + 416 cm 2 S.A. = 1,028 cm 2

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Surface Area of a Cube A cube has 6 congruent square faces. Find the area of one face, and multiply it by 6.

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Example 7 in A = s 2 A = 7 2 A = 49 in 2 S.A. = 49(6) S.A. = 294 in 2

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Surface Area of a Cylinder A cylinder consists of two circle bases and one rectangular side. The length of the rectangle is equal to the circumference of the circle. Find the area of the circles and add it to the area of the rectangle.

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Example 5 m 16 m Area of the circles A = r 2 A = 3.14(5 2 ) A = 3.14 (25) A = 78.5 m 2 2 circles: 78.5 x 2 = 157 m 2 Rectangle The width of the rectangle is the height of the cylinder (16 m). The length of the rectangle is the circumference of the circle. C = 2 r C = 2(3.14)(5) C = 31.4 m A = lw A = 31.4(16) A = 502.4 m 2

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Put the areas together: S.A. = 157 m 2 + 502.4 m 2 S.A. = 659.4 m 2

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Homework Time

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