8-7 Surface Area Learn to find the surface areas of prisms, pyramids, and cylinders.

8-7 Surface Area Vocabulary surface area net

8-7 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 the pattern made when the surface of a three-dimensional figure is layed out flat showing each face of the figure.

8-7 Surface Area Additional Example 1A: Finding the Surface Area of a Prism Find the surface area S of the prism. 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.

8-7 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 = = 188 Add the areas of each face. The surface area is 188 in 2.

8-7 Surface Area Additional Example 1B: Finding the Surface Area of a Prism Find the surface area S of each prism. 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.

8-7 Surface Area Additional Example 1B Continued Front: 9  7 = 63 Top: 9  5 = 45 Side: 7  5 =  2 =  2 =  2 = 70 S = = 286Add the areas of each face. The surface area is 286 cm 2.

8-7 Surface Area Check It Out: Example 1A Find the surface area S of the prism. 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. 3 in. 11 in. 6 in. 11 in. 6 in. 3 in. A B C DE F

8-7 Surface Area Check It Out: Example 1A A: A = 6  3 = 18 B: A = 11  6 = 66 C: A = 11  3 = 33 D: A = 11  6 = 66 E: A = 11  3 = 33 F: A = 6  3 = 18 S = = 234 Add the areas of each face. The surface area is 234 in in. 6 in. 3 in. A B C DE F

8-7 Surface Area Check It Out: Example 1B Find the surface area S of each prism. 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

8-7 Surface Area Check It Out: Example 1B Continued Side: 10  8 = 80 Top: 10  6 = 60 Front: 8  6 =  2 =  2 =  2 = 96 S = = 376Add the areas of each face. The surface area is 376 cm 2. 6 cm 10 cm 8 cm top front side

8-7 Surface Area The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

8-7 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 =  28 S = Substitute. S = s  ( bh) 1 2 __ S =  (  7  8) ‏ 1 2 __ S = 161 The surface area is 161 ft 2.

8-7 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 S = Substitute. S = s  ( bh) 1 2 __ S =  (  5  10) ‏ 1 2 __ S = 125 The surface area is 125 ft 2. 5 ft 10 ft 5 ft

8-7 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

8-7 Surface Area Additional Example 3: Finding the Surface Area of a Cylinder Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = area of curved surface + 2  (area of each base) ‏ Substitute. S = h  (2r) + 2  (r 2 ) S = 7  (2    4) + 2  (  4 2 ) ‏ ft

8-7 Surface Area Additional Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S  7  8(3.14) + 2  16(3.14) ‏ S  7   The surface area is about ft 2. Use 3.14 for . S  S  S = 7  8 + 2  16

8-7 Surface Area Check It Out: Example 3 Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = area of curved surface + 2  (area of each base) ‏ Substitute. S = h  (2r) + 2  (r 2 ) S = 9  (2    6) + 2  (  6 2 ) ‏ 6 ft 9 ft

8-7 Surface Area Check It Out: Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S  9  12(3.14) + 2  36(3.14) ‏ S  9   The surface area is about ft 2. Use 3.14 for . S  S  S = 9  12 + 2  36