Name Class Date. Draw a net that you think will make a cube on your graph paper, and then cut it out. Can you fold it into a cube?

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1 Name Class Date Surface Area Going Deeper Essential question: How can you use nets to find surface areas? A net is a two-dimensional pattern of shapes that can be folded into a three-dimensional figure. The shapes in the net become the faces of the three-dimensional figure. CC.6.G.4 EXPLORE Nets of a Cube video tutor A Copy the following nets on graph paper and cut them out along the blue lines. Net A Net B One of these nets can be folded along the black lines to make a cube. Which net will NOT make a cube? B See if you can find another net that can be folded into a cube. Draw a net that you think will make a cube on your graph paper, and then cut it out. Can you fold it into a cube? C Compare your results with several of your classmates. How many different nets for a cube did you and your classmates find? REFLECT How do you know that each net cannot be folded into a cube without actually cutting and folding it? 1a. 1b. 1c. What shapes will appear in a net for a rectangular prism that is not a cube? How many of these shapes will there be? Chapter Lesson 7

2 The surface area of a three-dimensional figure is the sum of the areas of its faces. A net can be helpful when finding surface area. 2 CC.6.G.4 EXPLORE Surface Area of a Rectangular Prism The gift wrap department of a store has specially sized boxes to wrap sweaters. Use the box s dimensions to label the dimensions of the net. Then find the surface area of the box Complete the table to find the surface area. Face Base (in.) Height (in.) Area ( in 2 ) Top Bottom Front Back Right Left Total The surface area of the sweater box is REFLECT 2a. How did you find the area of each face? square. 2b. If the box had been a cube, how would finding the surface area have been easier? Chapter Lesson 7

3 A pyramid is a three-dimensional figure whose base is a polygon and whose other faces are all triangles. A pyramid is named by its base. A pyramid whose base is a triangle is a triangular pyramid. A pyramid whose base is a square is a square pyramid, and so on. 3 CC.6.G.4 EXPLORE Surface Area of a Pyramid Find the surface area of the pyramid. 17 in. A How many faces does the pyramid have? B What polygon forms the base of the pyramid? 16 in. 16 in. What is the formula for the area of this polygon? A = in. in. C What polygon forms each of the other faces? What is the formula for the area of this polygon? D Complete the net by labeling its dimensions. E Complete the table to find the surface area. in. Face Base (in.) Height (in.) Area (i n 2 ) Base 16 Total The surface area of the pyramid is square. REFLECT 3a. What would have been a quicker way to find the combined areas of the triangles? 3b. Surface area is measured in square units. Why are square units used when working with a three-dimensional figure? Chapter Lesson 7

4 practice Identify the three-dimensional figure formed by each net Draw a net for each three-dimensional figure Find the surface area of each figure ft 20 in. 20 ft 8 ft 18 in. 16 in. square feet square Chapter Lesson 7

5 Name Class Date 8-7 Additional Practice Find the surface area S of each prism Find the surface area S of each pyramid A rectangular box has no top. It is 6 long, 4 wide, and 5 tall. What is the surface area of the box? 6. The surface area of a rectangular prism is 48 square feet. The area of its front is 4 square feet, and the area of one side is 10 square feet. What is the area of the top of the prism? Chapter Practice and Problem Solving

6 Problem Solving Write the correct answer. 1. Tara made fuzzy cubes to hang in her car. Each side of the 2 cubes is 4 long. How much fuzzy material did Tara use to make both cubes? 2. The top of the Washington Monument is a square pyramid covered with white marble. Each triangular face is 58 feet tall and 34 feet wide. About how many square feet of marble covers the top of the monument? (The base is hollow.) 3. The Parthenon, a famous temple in Greece, is surrounded by large stone columns. Each column is 10.4 meters tall and has a diameter of 1.9 meters. To the nearest whole square meter, what is the surface area of each column (not including the top and bottom)? 4. The tablet that the Statue of Liberty holds is 7.2 meters long, 4.1 meters wide, and 0.6 meters thick. The tablet is covered with thin copper sheeting. If the tablet was freestanding, how many square meters of copper covers the statue s tablet? Circle the letter of the correct answer. 5. The largest Egyptian pyramid is called the Great Pyramid of Khufu. It has a 756-foot square base and a slant height of 481 feet. What is the total surface area of the faces of the Pyramid of Khufu? A 727,272 ft 2 B 727,722 ft 2 C 727,727 ft 2 D 772,272 ft 2 6. A glass triangular prism for a telescope is 5.5 tall. Each side of the triangular base is 4 long, with a 3-inch height. How much glass covers the surface of the prism? F 6 in 2 G 12 in 2 H 39 in 2 J 78 in 2 Chapter Practice and Problem Solving