Surface Area and Volume
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1 15 CHAPTER Surface Area and Volume Lesson 15.1 Building Solids Using Unit Cubes How many unit cubes are used to build each solid? unit cubes unit cubes Extra Practice 5B 115
2 3. unit cubes unit cubes unit cubes 116 Chapter 15 Lesson 15.1
3 Lesson 15.2 Drawing Cubes and Rectangular Prisms Draw on dot paper. 1. Draw a unit cube. 2. Draw two different views of a rectangular prism made up of 2 unit cubes. 3. Draw a cube made up of 8 unit cubes. Extra Practice 5B 117
4 Draw these cubes or rectangular prisms on the dot paper Chapter 15 Lesson 15.2
5 Extra Practice 5B 119
6 Chapter 15 Lesson 15.2
7 Complete the drawing of each cube or rectangular prism Extra Practice 5B 121
8 Chapter 15 Lesson 15.2
9 Lesson 15.3 Find the surface area. Nets and Surface Area 1. The diagram shows the net of a cube. Find the surface area of the cube The diagram shows the net of a rectangular prism. Find the surface area of the rectangular prism Extra Practice 5B 123
10 The diagrams show the nets of cubes or rectangular prisms. Find the surface area of each cube or rectangular prism in Chapter 15 Lesson 15.3
11 Find the surface area of each cube or rectangular prism in in. 7 in in. 9 in. 6 in in. 6 in. 12 in Extra Practice 5B 125
12 Solve. Show your work. 13. The surface area of a cube is 216 square centimeters. Find the length of the cube. 14. A rectangular piece of wood has a length of 30 centimeters and a square base with sides that measure 6 centimeters. What is the surface area of the piece of wood? 15. An open rectangular water tank measures 20 inches by 18 inches by 16 inches. The tank is full of water. Find the total surface area of the tank that is in contact with the water. 20 in. 18 in. 16 in. 126 Chapter 15 Lesson 15.3
13 Lesson 15.4 Understanding and Measuring Volume These solids are formed by stacking unit cubes in the corner of a room. Find the volume of each solid. 1. Solid A Volume cubic units 2. Volume Solid B cubic units Extra Practice 5B 127
14 3. Solid C Volume cubic units 4. Volume Solid D cubic units Compare the volumes of the solids in Exercises 1 to 4. Then fill in the blanks. 5. Solid has the smallest volume. 6. Solid and Solid have the same volume. 128 Chapter 15 Lesson 15.4
15 These solids are formed by stacking unit cubes in the corner of a room. Find the volume of each solid. 7. Solid E 8. Volume 3 Solid F Volume 3 Extra Practice 5B 129
16 9. Solid G Volume Solid H Volume Chapter 15 Lesson 15.4
17 Compare the volumes of the solids in Exercises 7 to 10. Then fill in the blanks. 11. Solid has the smallest volume. 12. Solid has the largest volume. 13. Solid and Solid have the same volume. These solids are built using 1-centimeter cubes. Find the volume of each solid. Then fill in the blanks Length Length Width Width Height Height Volume 3 Volume 3 Extra Practice 5B 131
18 16. Length Width Height Volume Length Width Height Volume Chapter 15 Lesson 15.4
19 Lesson 15.5 Volume of a Rectangular Prism and Liquid Find the volume of each rectangular prism Length Width Height 2. Volume Length Width Height Volume 3 Extra Practice 5B 133
20 Find the volume of each rectangular prism Length Width Height 4. Volume Volume Chapter 15 Lesson 15.5
21 Volume 3 Find the length of the unknown edge of each rectangular prism ? Width 7.? Height Extra Practice 5B 135
22 ? 6 Length 9. The fi gure is a rectangular prism with a square base ? Length Write each measure in cubic centimeters ml L 125 ml L 600 ml L 80 ml L 50 ml L 6 ml 3 Write each measure in liters and milliliters or liters L ml 17. 1,850 3 L ml 18. 3,065 3 L ml L L 21. 1,650 3 L 22. 2,075 3 L 136 Chapter 15 Lesson 15.5
23 Find the volume of water in each rectangular tank in milliliters. Hint: ml Volume Volume Find the volume of water in each rectangular tank in liters. Hint: ml 1, L Volume 20 Volume 15 Extra Practice 5B 137
24 Solve. Show your work. 27. A rectangular fi sh tank measures 38 centimeters by 23 centimeters by 18 centimeters. How much water is in the tank when it is 2_ 3 -full? Give your answer in liters and milliliters A rectangular tank measuring 30 centimeters long, 22 centimeters wide, and 25 centimeters high is 4_ 5 -full of water. If 1_ 4 of the water is removed, what is the volume of water left in the tank? Give your answer in liters A rectangular tank measuring 42 centimeters by 20 centimeters by 24 centimeters is fi lled with water to a height of 7 centimeters. What is the volume of water needed to fi ll the tank completely? Give your answer in liters Chapter 15 Lesson 15.5
25 Put on Your Thinking Cap! Solve. Show your work. 1. Jessica used 35 unit cubes to build the solid shown. Another row of cubes is to be placed below the bottom row following the same pattern. How many more cubes will Jessica need? Extra Practice 5B 139
26 2. Paul uses 5 unit cubes to build the fi rst fi gure and 8 unit cubes to build the second fi gure into the T-shaped patterns shown. Pattern 1 Pattern 2 a. Paul continues to build the third and fourth patterns. Find the number of unit cubes in Patterns 3 and 4. Record your answers in the table. T-Shaped Pattern Number of Unit Cubes b. How many cubes would be used to build Patterns 5 and 6? c. Find the number of unit cubes in Pattern Chapter 15 Put on Your Thinking Cap!
27 3. The solid is made up of identical cubes glued together. The surface area of the solid is painted blue. The volume of the solid is 960 cubic centimeters. Find the surface area that is painted blue. 4. In order to fi ll the box completely, centimeter cubes are needed. What is the height of the box? ? 9 Extra Practice 5B 141
28 5. The solid is made up of 3-centimeter cubes. a. Find the volume of the solid. b. Find the surface area of the solid. c. The whole solid is painted red. i. Find the number of cubes that have only two faces painted red. ii. Find the number of cubes that have only three faces painted red. iii. Find the number of cubes that have only four faces painted red. 142 Chapter 15 Put on Your Thinking Cap!
29 6. Two wooden blocks, A and B, are glued together. The ratio of the volume of block A to the volume of block B is 3 : 7. a. What is the volume of block B? B A 6? b. What is the width of block B? Extra Practice 5B 143
30 7. A cubic container was completely fi lled with water. When 3_ 4 of the water from the container was poured into a rectangular tank, the tank became 1_ 4 full. The capacity of the tank is liters more than that of the cubic container. Find the length of the cubic container. water is poured into the tank Container Tank 8. John wanted to build a model wall measuring 36 centimeters long, 8 centimeters wide, and 21 centimeters high. He used blocks that measured 3 centimeters by 4 centimeters by 2 centimeters. John stopped after building 5_ 9 of the wall. How many more blocks will John need to complete the wall? 144 Chapter 15 Put on Your Thinking Cap!
31 9. How many 2-centimeter cubes can be packed into a rectangular prism measuring 25 centimeters by 15 centimeters by 20 centimeters? Cube Prism Identical watch boxes each measuring 10 centimeters by 8 centimeters by 6 centimeters are packed in a rectangular container measuring 54 centimeters by 44 centimeters by 22 centimeters. What is the maximum number of watch boxes that can be packed into the container? 10 Box Container Extra Practice 5B 145
32 11. Two identical rectangular cards measuring 20 centimeters by 12 centimeters are folded to form two different rectangular solids. a. One of the solids is shown below. Label its width and height. 12 b. Draw the other rectangular solid. Label its length, width, and height. c. Find the volume of each rectangular solid. 146 Chapter 15 Put on Your Thinking Cap!
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14 CHAPTER Surface Area and Volume Lesson 14.1 Building Solids Using Unit Cubes How many unit cubes are used to build each solid? 1. unit cubes 2. unit cubes Extra Practice 5B 121 3. unit cubes 4. 5. unit
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