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Holt CA Course 1 10-10 Surface Area Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

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Holt CA Course 1 10-10 Surface Area Warm Up Identify the figure described. 1. two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles prism pyramid

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Holt CA Course 1 10-10 Surface Area AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered: AF3.2 California Standards 1212

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Holt CA Course 1 10-10 Surface Area Vocabulary surface area net

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Holt CA Course 1 10-10 Surface Area The surface area of a three- dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.

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Holt CA Course 1 10-10 Surface Area The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface. To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. Helpful Hint

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Holt CA Course 1 10-10 Surface Area Additional Example 1: Finding the Surface Area of a Prism Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

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Holt CA Course 1 10-10 Surface Area Additional Example 1A Continued A: A = 5 2 = 10 B: A = 12 5 = 60 C: A = 12 2 = 24 D: A = 12 5 = 60 E: A = 12 2 = 24 F: A = 5 2 = 10 S = 10 + 60 + 24 + 60 + 24 + 10 = 188 Add the areas of each face. The surface area is 188 in 2.

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Holt CA Course 1 10-10 Surface Area Additional Example 1: Finding the Surface Area of a Prism Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

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Holt CA Course 1 10-10 Surface Area Additional Example 1B Continued Front: 9 7 = 63 Top: 9 5 = 45 Side: 7 5 = 35 63 2 = 126 45 2 = 90 35 2 = 70 S = 126 + 90 + 70 = 286 Add the areas of each face. The surface area is 286 cm 2.

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Holt CA Course 1 10-10 Surface Area Additional Example 2: Finding the Surface Area of a Pyramid Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = 49 + 4 28 S = 49 + 112 Substitute. S = s 2 + 4 ( bh) 1 2 __ S = 7 2 + 4 ( 7 8) 1 2 __ S = 161 The surface area is 161 ft 2.

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Holt CA Course 1 10-10 Surface Area Additional Example 3: Finding the Surface Area of a Cylinder Find the surface area S of the cylinder. Write your answer in terms of . S = area of curved surface + (2 area of each base) Substitute 7 for h and 4 for r. S = (h 2r) + (2 r 2 ) S = (7 2 4) + (2 4 2 ) ft S = (7 2 4)+ (2 16) Simplify the power.

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Holt CA Course 1 10-10 Surface Area Additional Example 3 Continued Find the surface area S of the cylinder. Write in terms of . S = (56 + 32) The surface area is about 88 ft 2. Multiply. S = 88 S = 56 + 32 Use the Distributive Property.

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Holt CA Course 1 10-10 Surface Area Check It Out! Example 1 Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces. 6 cm 10 cm 8 cm top front side

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Holt CA Course 1 10-10 Surface Area Check It Out! Example 1B Continued Side: 10 8 = 80 Top: 10 6 = 60 Front: 8 6 = 48 80 2 = 160 60 2 = 120 48 2 = 96 S = 160 + 120 + 96 = 376 Add the areas of each face. The surface area is 376 cm 2. 6 cm 10 cm 8 cm top front side

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Holt CA Course 1 10-10 Surface Area Check It Out! Example 2 Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = 25 + 4 25 S = 25 + 100 Substitute. S = s 2 + 4 ( bh) 1 2 __ S = 5 2 + 4 ( 5 10) 1 2 __ S = 125 The surface area is 125 ft 2. 5 ft 10 ft 5 ft

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Holt CA Course 1 10-10 Surface Area Check It Out! Example 3 Find the surface area S of the cylinder. Write your answer in terms of . S = area of lateral surface + (2 area of each base) Substitute 9 for h and 6 for r. S = (h 2r) + (2 r 2 ) S = (9 2 6) + (2 6 2 ) 6 ft 9 ft S = (9 2 6) + (2 36) Simplify the power.

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Holt CA Course 1 10-10 Surface Area Check It Out! Example 3 Continued Find the surface area S of the cylinder. Write your answer in terms of . S = (108 + 72) S = 180 The surface area is about 180ft 2. Multiply. S = 108 + 72 Use the Distributive Property.

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Holt CA Course 1 10-10 Surface Area Lesson Quiz Find the surface area of each figure. Use 3.14 as an estimate for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft 2 ≈188.4 ft 2 208 ft 2

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