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Preview Warm Up California Standards Lesson Presentation

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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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**AF3. 1 Use variables in expressions describing geometric quantities (e**

AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = pd–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 1 2

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Vocabulary surface area net

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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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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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**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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**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 Add the areas of each face. S = = 188 The surface area is 188 in2.

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**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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**Additional Example 1B Continued**

Front: 9 7 = 63 63 2 = 126 Top: 9 5 = 45 45 2 = 90 Side: 7 5 = 35 35 2 = 70 S = = 286 Add the areas of each face. The surface area is 286 cm2.

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**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 = s2 + 4 ( bh) 1 2 __ S = ( 7 8) 1 2 __ Substitute. S = 28 S = S = 161 The surface area is 161 ft2.

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**Additional Example 3: Finding the Surface Area of a Cylinder**

Find the surface area S of the cylinder. Write your answer in terms of . ft S = area of curved surface + (2 area of each base) S = (h 2r) + (2 r2) Substitute 7 for h and 4 for r. S = (7 2 4) + (2 42) S = (7 2 4)+ (2 16) Simplify the power.

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**Additional Example 3 Continued**

Find the surface area S of the cylinder. Write in terms of . S = 56 + 32 Multiply. S = ( )p Use the Distributive Property. S = 88p The surface area is about 88p ft2.

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

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**Check It Out! Example 1B Continued**

top side front 8 cm 10 cm 6 cm Front: 6 = 48 48 2 = 96 Top: 6 = 60 60 2 = 120 Side: 8 = 80 80 2 = 160 S = = 376 Add the areas of each face. The surface area is 376 cm2.

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**Find the surface area S of the pyramid.**

Check It Out! Example 2 Find the surface area S of the pyramid. 5 ft 10 ft S = area of square + 4 (area of triangular face) S = s2 + 4 ( bh) 1 2 __ S = ( 5 10) 1 2 __ Substitute. 10 ft S = 25 5 ft S = S = 125 The surface area is 125 ft2.

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**S = area of lateral surface + (2 area of each base)**

Check It Out! Example 3 Find the surface area S of the cylinder. Write your answer in terms of . 6 ft 9 ft S = area of lateral surface + (2 area of each base) S = (h 2r) + (2 r2) Substitute 9 for h and 6 for r. S = (9 2 6) + (2 62) S = (9 2 6) + (2 36) Simplify the power.

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**Check It Out! Example 3 Continued**

Find the surface area S of the cylinder. Write your answer in terms of . S = 108 + 72 Multiply. S = ( )p Use the Distributive Property. S = 180p The surface area is about 180p ft2.

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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 ft2 ≈188.4 ft2 208 ft2

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