Preview Warm Up California Standards Lesson Presentation

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

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

Vocabulary surface area net

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.

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

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.

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 = 10 + 60 + 24 + 60 + 24 + 10 = 188 The surface area is 188 in2.

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.

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 = 126 + 90 + 70 = 286 Add the areas of each face. The surface area is 286 cm2.

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 = 72 + 4  (  7  8) 1 2 __ Substitute. S = 49 + 4  28 S = 49 + 112 S = 161 The surface area is 161 ft2.

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  2r) + (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.

Additional Example 3 Continued Find the surface area S of the cylinder. Write in terms of . S = 56 + 32 Multiply. S = (56 + 32)p Use the Distributive Property. S = 88p The surface area is about 88p ft2.

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.

Check It Out! Example 1B Continued top side front 8 cm 10 cm 6 cm Front: 8  6 = 48 48  2 = 96 Top: 10  6 = 60 60  2 = 120 Side: 10  8 = 80 80  2 = 160 S = 160 + 120 + 96 = 376 Add the areas of each face. The surface area is 376 cm2.

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 = 52 + 4  (  5  10) 1 2 __ Substitute. 10 ft S = 25 + 4  25 5 ft S = 25 + 100 S = 125 The surface area is 125 ft2.

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  2r) + (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.

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 = (108 + 72)p Use the Distributive Property. S = 180p The surface area is about 180p ft2.

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