1. Warm Up Lesson Presentation Problem of the Day Lesson Quizzes
2. 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
3. Problem of the Day Which figure has the longer side and by how much: a square with an area of 81 ft 2 or a square with perimeter of 84 ft? a square with a perimeter of 84 ft; by 12 ft
4. Preview of MA.7.G.2.1 Justify and apply formulas for…surface area of…prisms, pyramids, cylinders… Sunshine State Standards
6. 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.
7. 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. 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 The surface area is 188 in 2 . Add the areas of each face.
9. 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.
10. 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 .
11. 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. 6 in. 3 in. 3 in. 3 in. 3 in. A B C D E F
12. 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 = 18 + 66 + 33 + 66 + 33 + 18 = 234 The surface area is 234 in 2 . 11 in. 6 in. 6 in. 3 in. 3 in. 3 in. 3 in. A B C D E F Add the areas of each face.
13. Check It Out: Example 1B Find the surface area S of each prism. Method 2: Use a three-dimensional drawing. 6 cm 10 cm 8 cm top front side Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.
14. 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
15. 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.
16. 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 S = 161 The surface area is 161 ft 2 . Substitute. S = s 2 + 4 ( bh ) 1 2 __ S = 7 2 + 4 ( 7 8 ) 1 2 __
17. 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 S = 125 The surface area is 125 ft 2 . 5 ft 5 ft 10 ft 10 ft 5 ft Substitute. S = s 2 + 4 ( bh ) 1 2 __ S = 5 2 + 4 ( 5 10 ) 1 2 __
18. 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
19. 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
20. 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 25.12 + 2 50.24 The surface area is about 276.32 ft 2 . Use 3.14 for . S 175.84 + 100.48 S 276.32 S = 7 8 + 2 16
21. 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
22. 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 37.68 + 2 113.04 The surface area is about 565.2 ft 2 . Use 3.14 for . S 339.12 + 226.08 S 565.2 S = 9 12 + 2 36
24. Lesson Quiz Find the surface area of each figure. Use 3.14 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
25. 1. Find the surface area of a rectangular prism with base length 7 ft, width 6 feet, and height 9 ft. A. 318 ft 2 B. 306 ft 2 C. 300 ft 2 D. 298 ft 2 Lesson Quiz for Student Response Systems
26. 2. Find the surface area of a cylinder with radius 5 ft and height 8 ft. Use 3.14 for A. 576.8 ft 2 B. 408.2 ft 2 C. 376.2 ft 2 D. 251.2 ft 2 Lesson Quiz for Student Response Systems
27. 3. Find the surface area of the figure shown. A. 162 ft 2 B. 152 ft 2 C. 142 ft 2 D. 132 ft 2 Lesson Quiz for Student Response Systems
