Surface Area and Volume
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1 Name: Chapter Date: Surface Area and Volume Practice 1 Building Solids Using Unit Cubes Find the number of unit cubes used to build each solid. Some of the cubes may be hidden unit cubes unit cubes unit cubes unit cubes unit cubes unit cubes Lesson 14.1 Building Solids Using Unit Cubes 187
2 Find the number of unit cubes used to build each solid. Some of the cubes may be hidden unit cubes unit cubes unit cubes unit cubes 11. unit cubes 188
3 Name: Date: Practice 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 two different solids made up of 3 unit cubes each. Lesson 14.2 Drawing Cubes and Rectangular Prisms 189
4 Draw each cube or rectangular prism on the dot paper. Example
5 Name: Date: Draw each cube or rectangular prism on the dot paper Draw a cube with edges 4 times as long as the edges of this unit cube. 9. Lesson 14.2 Drawing Cubes and Rectangular Prisms 191
6 Complete the drawing of each cube or rectangular prism
7 Name: Date: Practice 3 Prisms and Pyramids Identify the type of prism and the shapes of the faces. 1. This is a prism. 2. Two of its faces are. 3. Three of its faces are. 4. This is a prism. 5. All its faces are. Lesson 14.3 Prisms and Pyramids 193
8 Complete the table. Type of Prism Number of Faces Number of Edges Number of Vertices Identify the type of pyramid and the shape of the faces. 9. This is a pyramid. 10. All its faces are. 194
9 Name: Date: Identify the type of pyramid and the shapes of the faces. 11. This is a pyramid. 12. One of its faces is a. 13. Four of its faces are. Complete the table. Type of Pyramid Number of Faces Number of Edges Number of Vertices Lesson 14.3 Prisms and Pyramids 195
10 Name the solid formed by each net
11 Name: Date: Practice 4 Nets and Surface Area Find the surface area of each cube. Example 1. 5 in. 3 cm 3 cm 3 cm 5 in = = 54 Surface area of cube = 54 cm in. 12 in. 18 cm 12 in. 12 in. 18 cm 18 cm Lesson 14.4 Nets and Surface Area 197
12 Find the surface area of each rectangular prism. Example 22 in = = = = 592 Surface area of rectangular prism = 592 in. 2 8 in. 4 in in. 12 in. 15 in m 8 m 19 m 198
13 Name: Date: Find the surface area of each triangular prism. Example 3 in. 4 in. 18 in. 5 in = = = = = 228 Surface area of triangular prism = 228 in cm 24 cm 35 cm 5 cm Solve. Show your work. 7. Jeffrey cuts out the net of a box he wants to make. Find the surface area of the box. 8 in. 15 in. 8 in. 8 in. 10 in. Lesson 14.4 Nets and Surface Area 199
14 Solve. Show your work. 8. This glass fish tank does not have a cover. Find the total area of the glass panels used to make the tank. 27 cm 24 cm 21 cm 9. The tank shown is made of steel. It does not have a cover. Find the area of steel sheet used to make the tank ft 28 ft 13 ft 10. A rectangular piece of poster board measures 60 centimeters by 80 centimeters. Linn draws the net of a box on the poster board and cuts it out. If the box measures 10 centimeters by 16 centimeters by 27 centimeters, what is the area of the poster board left? 200
15 Name: Date: Practice 5 Understanding and Measuring Volume These solids are formed by stacking unit cubes in the corner of a box. Find the volume of each solid Volume cubic units Volume cubic units Volume cubic units Volume cubic units Lesson 14.5 Understanding and Measuring Volume 201
16 These solids are formed by stacking 1-centimeter cubes in the corner of a box. Find the volume of each solid Volume cm 3 Volume cm Volume cm 3 Volume cm Volume cm 3 Volume cm 3
17 Name: Date: These solids are built using 1-centimeter cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks. 11. A B Volume cm 3 Volume cm 3 Solid has a greater volume than solid. These solids are built using 1-meter cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks. 12. C D Volume m 3 Volume m 3 Solid has a lesser volume than solid. Lesson 14.5 Understanding and Measuring Volume 203
18 These solids are built using 1-inch cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks. 13. E F Length in. Length in. Width in. Width in. Height in. Height in. Volume in. 3 Volume in. 3 Solid has a lesser volume than solid. These solids are built using 1-foot cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks. 14. G H Length ft Length ft Width ft Width ft Height ft Height ft Volume ft 3 Volume ft Solid has a greater volume than solid.
19 Name: Date: Practice 6 Volume of a Rectangular Prism and Liquid Write the length, width, and height of each rectangular prism or cube. Example 5 cm 8 cm 6 cm Length Width Height cm cm cm ft 20 ft 12 ft 16 in. Length Width Height Length Width ft ft ft in. in. Height in. 25 in. 12 in. 3. Length m 18 m Width m 18 m Height m 18 m Lesson 14.6 Volume of a Rectangular Prism and Liquid 205
20 Find the volume of each rectangular prism cm 12 cm 5 cm The length of the rectangular prism is centimeters. The width of the rectangular prism is centimeters. The height of the rectangular prism is centimeters. Volume of the rectangular prism length width height cm in. 4 in. 2 in. 5 yd 8 yd 3 yd Volume Volume 206
21 Name: Date: Find the volume of each rectangular prism or cube ft 8. 4 ft 6 ft 16 m 16 m 16 m Volume Volume cm 4 cm 4 cm Volume in. Volume 9 in. 3 in in. 8 m 8 in. 7 in. 3 m 5 m Volume Volume Lesson 14.6 Volume of a Rectangular Prism and Liquid 207
22 Find the volume of each rectangular prism. Length Width Height Volume cm 12 cm 9 cm in. 25 in. 14 in m 12 m 8 m ft 10 ft 15 ft Solve. Show your work. 17. Find the volume of a cube with edges measuring 9 centimeters. 18. A rectangular prism has a length of 8 feet and a height of 5 feet. Its length is twice its width. Find the volume of the rectangular prism. 19. The base of a rectangular prism is a square whose sides each measure 9 inches. The height of the rectangular prism is 11 inches. Find its volume. 208
23 Name: Date: Find the volume of each rectangular prism. Example B 120 cm 2 h 8 cm Volume = area of base x height = 120 x 8 = 960 cm h 6 m 21. B 56 m 2 h 9 ft B 16 ft 2 Lesson 14.6 Volume of a Rectangular Prism and Liquid 209
24 22. h 10 in. B 48 in h 5 cm B 57 m 2 Solve. Show your work. 24. A rectangular box has a height of 15 meters. The area of its base is 210 square meters. Find the volume of the box. 25. Gerald s rectangular container has a height of 6 feet and a base area of 72 square feet. How much water would it take to fill the container to the brim? 210
25 Name: Date: Practice 7 Volume of a Rectangular Prism and Liquid Write each measure in milliliters cm cm ,000 cm ,600 cm 3 Write each measure in cubic centimeters ml L ml O 7. 3 L T 9 2 L 125 ml E L 50 ml Y L S L 60 ml W L 2 ml N Do you know which national park is the oldest in the United States? Match the letters to the answers to find out. 10,050 2, ,060 15,000 3, ,002 2,125 National Park Write each measure in liters and milliliters cm ,000 cm ,050 cm ,470 cm ,801 cm ,003 cm ,600 cm ,075 cm 3 Lesson 14.6 Volume of a Rectangular Prism and Liquid 211
26 Find the volume of water in each rectangular tank in milliliters. (Hint: 1 cm 3 = 1 ml) cm 12 cm 4 cm 9 cm 7 cm 5 cm Volume Volume Find the volume of water in each rectangular tank in liters and milliliters. (Hint: 1,000 cm 3 = 1 L) cm 25 cm 8 cm cm 28 cm 6 cm Volume Volume cm 18 cm 9 cm 7 cm 26 cm 8 cm 212 Volume Volume
27 Name: Date: Solve. Show your work. 27. How much water is in this tank when it is 1 3 full? 9 cm 12 cm 6 cm 28. This rectangular tank is filled with water to a height of 4 centimeters. How much more water is needed to fill the tank completely? 6 cm 4 cm 18 cm 12 cm Lesson 14.6 Volume of a Rectangular Prism and Liquid 213
28 Solve. Show your work. 29. A cubical tank with an edge length of 20 centimeters is filled with 3.75 liters of water. How much more water is needed to fill the tank completely? Give your answer in liters. 20 cm 20 cm 20 cm 30. The rectangular tank shown is 1 -filled with water. Then another 4 1 liter 400 milliliters of water is added. Find the volume of water in the tank in the end. Give your answer in liters and milliliters. 8 cm 20 cm 28 cm 214
29 Name: Date: Solve. Show your work. 31. This container is half-filled with oil. What is the volume of oil in the container? Give your answer in liters and milliliters. 19 cm 14 cm 14 cm 32. A cubical tank whose edges each measure 12 centimeters is half-filled with water. The water is poured into an empty rectangular tank measuring 10 centimeters by 8 centimeters by 7 centimeters until it is full. How much water is left in the cubical tank? Give your answer in milliliters. 12 cm 12 cm 12 cm 7 cm 10 cm 8 cm Lesson 14.6 Volume of a Rectangular Prism and Liquid 215
30 Solve. Show your work. 33. The rectangular swimming pool shown contains 600 cubic meters of water. How much more water has to be added so that the water level is 1 meter from the top? 3 m 30 m 50 m 34. The rectangular tank shown is filled completely with water. How much water must be taken out so the height of the water level in the tank is 10 centimeters? Give your answer in milliliters. 15 cm 8 cm 6 cm 216
31 Name: Date: Solve. Show your work. 35. The large rectangular tank shown is 4 -filled with water. 5 The water is then poured into the smaller rectangular container until it is full. How much water is left in the tank? Give your answer in liters and milliliters. 12 cm 15 cm 15 cm 6 cm 8 cm 5 cm Lesson 14.6 Volume of a Rectangular Prism and Liquid 217
32 36. Water flows into this tank at 8 liters per minute. How long will it take to fill the tank? 20 cm 50 cm 60 cm 218
33 Name: Date: Practice 8 Find the volume of each solid figure. Volume of Composite Solids Example 6 cm A 5 cm B 6 cm 4 cm 2 cm Volume of prism A = = 120 cm 3 Volume of prism B = = 48 cm 3 Volume of the solid = = 168 cm ft 10 ft A B 9 ft 5 ft 5 ft Volume of prism A 5 Volume of prism B 5 Volume of the solid ft 3 Lesson 14.7 Volume of Composite Solids 219
34 2. 15 m 15 m A B 30 m 10 m 5 m Volume of prism A 5 Volume of prism B 5 Volume of the solid m 3 Solve. Show your work in. 5 in. 12 in. 9 in. 8 in cm 4 cm 16 cm 10 cm 5 cm Volume 5 Volume 5 220
35 Name: Date: 5. A rectangular block of wood is cut into two pieces, as shown below. What is the total volume of the block of wood? 5 ft 8 ft 2 ft 5 ft Lesson 14.7 Volume of Composite Solids 221
36 Solve. Show your work. 6. A shelf is made up of two rectangular pieces of metal. What is the total volume of metal in the shelf? 25 cm 30 cm 4 cm 8 cm 5 cm 222
37 Name: Date: This rectangular container is 2 -filled with water. 5 How much more water is needed to increase the height of the water level to 3 centimeters? Show two methods of solving this problem. Which method do you prefer? Why? 5 cm 8 cm 10 cm 223
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39 Name: Date: Put On Your Thinking Cap! Challenging Practice Find the number of cubes in each prism cubes cubes Each solid is cut vertically along the line shown. Draw an additional line to complete the two shapes. Then, identify the solid shapes that result
40 5. A rectangular tank is half-filled with water. Another 650 cubic centimeters of water are needed to make it 3 full. How much water will be in the 5 tank when it is 3 5 full? 6. A cube has a surface area of 216 square centimeters. A second cube has edges that are 3 times as long. How much greater is the surface area of the second cube than the first cube? 226
41 Name: Date: Put On Your Thinking Cap! Problem Solving You may trace, cut out, and fold the nets. Which of these are nets of a cube? Check the boxes
42 9. A prism has a square base whose edges each measure 5 centimeters. The ratio of its height to its width is 4 : 1. Find the volume of the rectangular prism in cubic centimeters. height 5 cm 228
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