Geometry: Volume Practice 28 Everything made in The Cubic Factory is in the shape of a cube. They sell cubic puzzles, cubic games, cubic calendars, and even cubic books. Help the factory package its unusual products. Reminders • A cube has the same length, width, and height. • The volume of a figure is computed by multiplying the length times the width times the height. Formula: V = (l x w) x h 1. The cubic factory sells a giant cubic puzzle which is 6 inches long, 6 inches wide, and 6 inches high. What is the volume of the puzzle in cubic inches? _______________ 2. The factory sells cubic puzzles which are 3 centimeters long, 3 centimeters wide, and 3 centimeters high? What is the volume of the puzzle in cubic centimeters? _______________ 3. One cubic board game is 9 inches high, 9 inches wide, and 9 inches long. What is the volume in cubic inches? _______________ 4. One cubic puzzle is 2 inches on each side. What is the volume in cubic inches? ______________ 5. The factory sells a cubic flashlight which is 5 inches on each side. What is the volume?________ 6. The Cubic Factory needs to package its one-inch cubic puzzles in large boxes which are 9 inches long, 10 inches wide, and 10 inches high. How many cubic puzzles could they fit in each box? _______________ 7. The factory packages its one-inch cubic magnifying glasses in boxes which are 4 inches wide, 8 inches long, and 6 inches high. How many cubic magnifying glasses could they fit into each box? _______________ 8. The factory packages cubic centimeter wooden blocks in boxes which are 10 centimeters long, 10 centimeters wide, and 10 centimeters high. How many cubic centimeter blocks could they fit into each box? _______________ 9. The factory packages its one-cubic foot games in huge boxes which are 4 feet long, 5 feet wide, and 6 feet high. How many cubic foot games can they fit into each box? _______________ 10. How many one-inch cubic puzzles can the factory fit into a box which is a cubic foot (1 foot long, 1 foot wide, and 1 foot high)? _______________ 31 Answer Key 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. no 5 m.p.h. 20 m.p.h. the scale doesn’t go 0 to 70 start at 0/use a different scale 1995 1998 10 thousand dollars the scale is distorted, starts at 40 25 thousand dollars scale starts at 40 thousand dollars starts at 0 and go to 70 Page 27 1. 920 feet 48,000 feet2 2. 288 feet 4,700 feet2 3. 360 feet 8,100 feet2 4. 600 feet 20,000 feet2 5. 320 yd. 6,000 yd.2 6. 260 feet 4,225 feet2 7. 346 m 7,300 m2 8. 350 yd. 7,150 yd.2 Page 28 1. 240 feet2 2. 450 feet2. 3. 1,035 feet2 4. 240 feet2 5. 4,171 feet2 6. 1,155 feet2 7. 672 feet2 8. 87.5 feet2 9. 99.6 feet2 10. 484 feet2 Page 29 1. C = πd C = 3.14 x 9 28.26 centimeters 2. C = πd C = 3.14 x 23 72.22 centimeters 3. C = 2πr C = 2 x 3.14 x 2 12.56 centimeters (cont.) 4. C = πd C = 3.14 x 2 6.28 centimeters 5. C = πd C = 3.14 x 2.6 8.164 centimeters 6. C = 2πr C = 2 x 3.14 x 12 75.36 inches 7. C = 2πr C = 2 x 3.14 x 2 12.56 inches 8. C = 2πr C = 2 x 3.14 x 3 18.84 centimeters Page 30 1. A = πr2 A = 3 x 3 x 3.14 28.26 cm2 2. A = πr2 A = 3.14 x 8 x 8 200.96 inches2 3. A = πr2 A = 3.14 x 6 x 6 113.04 cm2 4. A = πr2 A = 3.14 x 7 x 7 153.86 millimeters2 5. A = πr2 A = 3.14 x 9 x 9 254.34 millimeters2 6. A = πr2 A = 3.14 x 2 x 2 12.56 feet2 7. A = πr2 A = 3.14 x 4 x 4 50.24 feet2 8. A = πr2 A = 3.14 x 4.5 x 4.5 63.585 cm2 9. A = πr2 A = 3.14 x 3.5 x 3.5 38.465 cm2 10. A = πr2 A = 3.14 x 1.15 x 1.15 4.15265 cm2 Page 31 1. 216 inches3 2. 27 cm3 3. 729 inches3 4. 8 inches3 5. 125 inches3 6. 900 cubic puzzles 7. 192 cubic magnifying glasses 8. 1,000 cm3 blocks 9. 120 games 10. 1,728 cubic puzzles Page 33 1. library 2. town hall 3. gas station 4. (-11, 1) 5. (4, -4) 6. (-5, -9) 7. park 8. (-10, -7) 9. (-9, 5) 10. general store 11. drug store 12. III 13. I 14. II Page 34 1. 3/10 2. 4/15 3. 9/50 4. 11/16 5. 1/2 6. 7. 8. 9. 10. 3/40 2/3 8/45 2/5 1/27 Page 35 1. n = 35 – 12 n = 23 2. 23 + n = 41 n = 18 3. n – 29 = 61 n = 90 4. 36 + n = 53 n = 17 5. 19 + n = 43 n = 24 6. n/4 = 12 n = 48 7. n x 12 = 96 n=8 8. n/8 = 11 n = 88 9. n x 19 = 190 n = 10 10. 42/n = 6 n=7 Page 36 1. 5:4 or 5/4 2. 4:5 or 4/5 3. 2:5 or 2/5 4. 5:2 or 5/2 5. 3:5 or 3/5 6. 5:3 or 5/3 7. 4:3 or 4/3 8. 9. 10. 11. 12. 13. 14. 15. 3:4 or 3/4 2:3 or 2/3 3:2 or 3/2 7:5 or 7/5 5:7 or 5/7 3:7 or 3/7 7:3 or 7/3 12:2 or 12/2 or 6:1 or 6/1 16. 2:12 or 2/12 or 1:6 or 1/6 17. 3:7 or 3/7 18. 7:3 or 7/3 Page 37 1. 1:4 :: 20:n n = 80 feet 2. 1:2 :: 25:n n = 50 feet 3. 3:15 :: 9:n n = 45 m 4. 4:1 :: 100:n n = 25 stories 5. 3:10 :: 33:n n = 110 yd. 6. 3:10 :: 15:n n = 50 m 7. 5:3 :: n:30 n = 50 inches 8. 7:2 :: 42:n or 2:7 :: n:42 n = 12 inches Page 38 1. 528 9 59 (58.67) 2. 911 11 83 (82.8) 3. 1,160 13 89 (89.2) 4. 138 10 14 (13.8) 5. 63 12 5 (5.25) 6. 175 13 13 (13.46) 7. 109 16 7 (6.8) Page 39 1. (46, 47, 48, 49, 50, 52, 52, 52, 53, 54, 2. 3. 4. 5. 56) 52 52 (47, 49, 55, 56, 57, 58, 59, 59, 59, 60, 60, 61, 63) 59 59 (57, 59, 59, 60, 61, 61, 63, 63, 65, 66) 59, 61, 63 61 (47, 49, 49, 49, 51, 52, 53, 54, 55, 57, 59) 49 52 (39, 40, 44, 44, 45, 48, 50, 55, 57, 57, 58, 60, 60, 61) 44, 57, 60 52.5 Page 40 1. C 2. D 3. B 4. A 5. A 6. 7. 8. 9. 10. C B D B D Page 41 1. B 2. D 3. C 4. A 5. D 6. 7. 8. 9. 10. A C A B C Page 42 1. A 2. B 3. C 4. B 5. D 6. 7. 8. 9. 10. B D C A D Page 43 1. C 2. C 3. B 4. D 5. D 6. 7. 8. 9. 10. B A D B C Page 44 1. C 2. C 3. A 4. B 5. D 6. 7. 8. 9. 10. A C B D C Page 45 1. C 2. A 3. B 6. C 7. A 8. B 48 Unit 6: Systems of Equations Name _____________________________________ Measurement Review (Systems Unit) Directions: Show your work neatly. 141 Appendix B: Answer Keys Guided Practice Book Answers (cont.) 81 Fill It Up 6.10 Name _________________________________________ Date ___________________ Part A Count the number of cubic units in each figure. Remember to count the cubic units you cannot see. Then write the volume of each figure in cubic units. 1. 2. 3. 4. For problems 5–10, round your answer to the nearest whole number. 6. Find the volume. 5. Find the volume. h = 11.3 mm h = 11.3 mm h = 11.3 mm l = 4.8 mm w = 13 mm h = 11.3 mm 7. Find the volume. 8. Find the length of the side of this cube. r = 5.6 in. V = 2,197 ft.3 h = 8.2 in. 10. Find the volume. 9. Find the height of the rectangular prism. r = 1.136 m V = 108 in.3 l = 9 in. w = 4 in. h = 2.321 m h = _______ 81 Answer Key Student Pages Page 53 Page 63 1. 1 m = 100 cm, 1 kg = 1,000 g, 1 cm = 10 mm 2. 1 km = 1,000 m, 1 ton = 1,000 kg, 1 L = 1,000 mL 3. 1 km = 100,000 cm, 1t = 1,000,000 g, 1 L = 1,000 cm 4. To convert cm to km, we divide by 1,000. 5. To convert g to kg, we divide by 1,000. 6. To convert mL to L, we divide by 1,000. 7. 25 km 8. 740 cm 9. 9,600 g 10. 0.72 m 11. 140 mm 12. 0.180 kg 13. 8,600 g 14. 716.542 tons 15. 9,210 kg 16. 16,240 mL 17. 1.21 m 18. 5,100 mL 19. 8 cups 20. 4 pints 21. 2 quarts 22. 12 gallon 23. 6000 pounds 24. 6000 pounds 25. 2640 feet 26. 2640 feet 1. 2. 3. 4. 5. 6. 7. 8. Area 135 sq. ft. 1,024 sq. in. 228 sq. yards 1,936 sq. m 448 sq. in. 2,862 sq. yards 29.6 sq. in. 361 sq. yards Page 69 Answers will vary. Page 75 1. 2. 3. 4. 5. 6. 7. 8. 1,368.1 cm2 110.8 in.2 244.9 m2 420 yards2 655.2 ft.2 2.4 yards2 967.1 m2 483.7 in.2 Page 81 Part A 1. 10 units cubed 2. 9 units cubed 3. 28 units cubed 4. 48 units cubed 5. 1,443 mm cubed 6. 705 mm cubed 7. 807 in. cubed 8. 13 ft. 9. 3 in. 10. 9 in. cubed 120 Perimeter 48 ft. 128 in. 62 yards 176 m 128 in. 266 yards 22.8 in. 76 yards 4 How to Facts to Know • • • Compute the Volumes of Rectangular Prisms and Cylinders Volume of a Rectangular Prism To determine how much material can fit into an empty rectangular object such as a box or in any other rectangular prism: length = 4 cm 1. Measure the length, the width, and the height of the prism. height = 2 cm 2. Multiply the length times the width times the width = 3 cm height. 3. Record the answer in cubic units. 4. The formula is V = l x w x h or Volume = length x width x height 5. The answer is V = 4 cm x 3 cm x 2 cm = 24 cubic centmeters (or cm3) Cubic Units • A cubic foot is 1 foot long, 1 foot wide, and 1 foot high. 1 in. 1 in. 1 in. • A cubic centimeter is 1 centimeter long, 1 centimeter wide, and 1 centimeter high. 1 in. 1 in. • A cubic inch is 1 inch long, 1 inch wide, and 1 inch high. Volume of a Cylinder A cylinder is a round tube with two circular, flat faces. You can compute the volume of a cylinder this way: 2. Multiply this area times the length (or height) of the cylinder. 3. The formula is V = π(r2) x h 4. The answer is V = 3.14 x (4)2 x 8 = 401.92 cubic meters (or m3). 17 r=4m 8m 1. Multiply the radius times itself and this product times pi (3.14) to compute the area of the circular face. 1 in. 4 Practice • • • • • • • • • • • Computing the Volumes of Rectangular Prisms 5 ft. V=lxwxh The formula for the volume of a rectangular prism is V = 5 ft. x 3 ft. x 2 ft. V = 30 ft.3 2 ft. 3 ft. The answer is always expressed in cubic units. Directions: Use the information on page 17 to compute the volume of each figure represented below. 10 ft. 5m 1. 2. 9 ft. 7m 8 ft. V = ______ 3m V = ______ 7 cm 3. 11 in. 4. 7 cm 5 in. 3 in. 7 cm V = ______ V = ______ 10 yd. 5. 6. 8 yd. 7.6 m 4.2 m 2.1 m 3 yd. V = ______ V = ______ 7. What is the volume of a box which is 5.6 m long, 7.2 m wide, and 2.3 m high? V = ______ 8. What is the volume of a prism 9.1 cm long, 10.6 cm wide, and 7.2 cm high? V = ______ 9. What is the volume of a prism which is 12 feet long, 12 feet wide, and 12 feet high? V = ______ 10. What is the volume of a prism 3 1– feet long, 5 1– feet wide, and 4 1– feet high? V = ______ 2 2 2 18 4 Practice • • • Computing the Volumes of Cylinders This is the formula for computing the volume of a cylinder: V = πr2 x h r = 3 cm • Multiply the radius times itself. • Multiply that product times 3.14. h = 4 cm • Multiply that product times the height. • Express the answer in cubic units. V = πr2 x h V = 3.14 x 3 cm x 3 cm x 4 cm r = 3 cm V = 113.04 cm3 Directions: Use the information on page 17 to compute the volume of each cylinder. Remember to indicate the units—cubic feet, cubic meters, cubic inches, etc.—with the answer. 1. r = 1 in. r=4m 4. h = 6 in. h=7m V = ______ V = ______ r = 1 cm 5. 2. r = 20 cm h = 3 cm h = 40 cm V = ______ V = ______ r = 3 cm 6. 3. r = 7 ft. h = 10 cm h = 10 ft. V = ______ V = ______ 19 4 Practice • • • • • Applying Volume Measurements to Real-Life Applications Directions: Find the objects listed in the problems below in your classroom or your house. Find the length, width, and height of these objects and then calculate the volume of each object in cubic inches. 1. pencil box 3. tabletop l = _____ in. 2. storage box l = _____ in. w = _____ in. w = _____ in. h = _____ in. h = _____ in. V = _____ in.3 V = _____ in.3 4. tissue box l = _____ in. l = _____ in. w = _____ in. w = _____ in. h = _____ in. h = _____ in. V = _____ in.3 V = _____ in.3 Directions: Find the objects listed below in your classroom or home. Measure the radius and height of each object and calculate the volume. h = _____ in. 5. soup can 7. soda can h = _____ in. r = _____ in. r = _____ in. Soda pop V = _____ in.3 V = _____ in.3 Soup 6. candle h = _____ in. 8. hair spray can r = _____ in. h = _____ in. r = _____ in. hair spray V = _____ in.3 V = _____ in.3 7. What is the volume of a cylinder with a radius of 10.2 cm and a length of 20 cm? _____________ 8. What is the volume of a cylinder with a radius of 15.5 m and a volume of 90 m? ______________ 20 • • • • • • • • • • • • • • • • • • • • • • Answer Key Page 6 5. 405 in.2 1. 5 11⁄16" 6. 49.14 m2 2. 2 5⁄16" 7. 116.39 cm2 3. 6 3/4" 8. 86.45 m2 4. 6 7/16" Page 16 5.–18. Answers will vary. 1. 50.24 m2 Pages 7 and 8 2. 78.5 cm2 Answers will vary. 3. 314 cm2 4. 452.16 cm2 Page 10 5. 1,256 cm2 1. 18.2 cm 6. 615.44 ft.2 2. 26.2 cm 7. 706.5 in.2 3. 131⁄2 cm 8. 1,962.5 m2 4. 161⁄2 ft. 5. 151⁄4 in. Page 18 6. 183⁄8 cm. 1. 105 m3 7.–10. Answers will vary. 2. 720 ft.3 3. 343 cm3 Page 11 4. 165 in.3 1. 15.6 cm 5. 240 yd.3 2. 111⁄4 in. 6. 67.032 m3 3. 24.4 m 7. 92.736 m3 4. 183⁄4 ft. 8. 694.512 cm3 5. 74.4 m 9. 1,728 ft.3 6. 64 yd. 10. 86 6/8 ft.3 7. 137.4 cm 8. 105.3 m Page 19 1. 351.68 m3 Page 12 2. 169.56 cm3 1. 19.1 m 3. 282.6 cm3 2. 22.6 m 4. 18.84 in.3 3. 26 in. 5. 50,240 cm3 4. 201⁄2 ft. 6. 1,538.6 ft.3 5. 25.12 m 6. 37.68 in. Pages 20–23 7. 31.4 cm Answers will vary. 8. 21.98 m Page 24 Page 14 1. 6 lbs. 4 oz. 2 1. 41 m 2. 1 ton 300 lbs. 2. 126 yd.2 3. 4,000 cassettes 3. 67.5 cm2 4. 100 pills 4. 6.08 m2 5. 100,000 pills 2 5. 34 ft. 6. 2,000 dictionaries 6. 16 1/4 in.2 7. 12,000 staplers 7. 3,680 m2 8. 100 people 8. 7,500 mm2 9. 500 mg or 1/2 g 10. 220 kg Page 15 11. 4,400 kg 1. 24 ft.2 12. 2,200 clips 2. 45 yd.2 13. 6,400 calculators 3. 11.66 cm2 14. 40 cameras 4. 27.72 cm2 Page 26 1. 8 fl. oz. 2. 16 fl. oz. 3. 32 fl. oz. 4. 48 fl. oz. 5. 64 fl. oz. 6. 72 fl. oz. 7. 32 fl. oz. 8. 64 fl. oz. 9. 160 fl. oz. 10. 96 fl. oz. 11. 4 qt. 12. 16 qt. 13. 128 fl. oz. 14. 60 qt. 15. 1,920 fl. oz. 16. 16 fl. oz. 17. 48 fl. oz. 18. 112 fl. oz. 19. 40 pints 20. 176 cups 21. 120 pints 22. 1,280 fl. oz. 23. 34 cups 24. 176 fl. oz. 25. 344 fl. oz. Page 27 1. 30 mL 2. 240 mL 3. 1,000 mL 4. 960 mL 5. 40 mL 6. 480 mL 7. 3,840 mL 8. 3.84 L 9. 38.4 L 10. 69.1 L 11. 960 L 12. 96 L 13. 96 L 14. 1920 15. 360 L Page 28 1. 2 qt. 2. 12 mL 3. 80 mL 4. 336 mL 5. 50 pennies 6. 432 mL 47 7. 8. 9. 10. 11. 12. 24 fl. oz. 384 mL 128 quarters 19.2 L 8 times 48 cups Page 30 1. 40° acute 2. 120° obtuse 3. 180° straight 4. 90° right 5. 50° acute 6. 130° obtuse 7. 250° reflex 8. 215° reflex 9. 90° right 10. 80° acute Page 31 1. <BAC = 100° 1. <CBA = 35° 1. <ACB = 45° 1. ▲ABC = 180° 2. <CDE = 50° 1. <ECD = 70° 1. <DEC = 60° 1. ▲DEC = 180° 3. <LMN = 90° 1. <MNL = 30° 1. <MLN = 60° 1. ▲LMN = 180° 4. <MNO = 25° 1. <OMN = 65° 1. <MON = 90° 1. ▲MNO = 180° 5. <XYZ = 60° 1. <ZXY = 60° 1. <YZX = 60° 1. ▲XYZ = 180° 6. <WPO = 154° 1. <POW = 11° 1. <PWO = 15° 1. ▲WPO = 180° 9 How to • • • • • • • • • • • Find the Volumes of Solids Facts to Know Plane geometry involves measuring flat or two-dimensional figures. Solid geometry is measuring figures with three, instead of two, dimensions—length, width, and height. r h h h w w l l One way to measure how much an object can hold is to measure its volume. The unit used to measure volume is a cube. The cube may be 1 cm on each side (a cubic centimeter), 1 in. on each side (a cubic inch), 1 ft. on each side (a cubic foot), etc. Imagine that each one of the small squares is a cubic inch. Adding them all up would give you the volume in cubic inches of this cube. Finding the Volume of Rectangular Solids To find the volume of a rectangular solid, use the formula Volume = l (length) x w (width) x h (height) or V = lwh. So volume is simply the area of the base rectangle times the height. Here’s an example: 4" Step 1: Put the numbers in the formula, V = lwh. Step 1: V = 10 x 4 x 7 7" Step 2: Multiply the numbers. Step 1: V = 40 x 7 Step 1: V = 280 cubic inches or 280 in.3 10" 38 9 How to Facts to Know (cont.) • • • • • • • • • • • Find the Volumes of Solids Finding the Volume of Cubes A cube has six equal sides. The length, width, and height are all equal. The formula for finding the volume of a cube is s3 (side x side x side). Another way of looking at it is s3 is really the area of the base (s2) x the height (s). Here’s an example: Step 1: Put the numbers in the formula, V = s3. Step 1: V = 43 Step 1: V = 4 x 4 x 4 Step 2: Multiply the numbers. Step 1: V = 16 (4) Step 1: So, V = 64 cubic inches or 64 in.3 4" 4" 4" Finding the Volume of Cylinders The top and bottom of a cylinder are circles, but the side of the cylinder “unrolls” or flattens out into a rectangle. 3 cm (radius) • • 3 cm 10 cm (height) 10 cm • 3 cm The formula for finding the volume of a cylinder is V = π (pi) x r (radius squared) x h (height) or V = π r2h. Find the volume of the cylinder above. (Remember that π is roughly equal to 3.14.) Step 1: Put the numbers in the formula: V = π r2 h. Step 1: V = 3.14 x 32 x 10 Step 1: V = 3.14 x 9 x 10 39 Step 2: Multiply the numbers. Step 1: V = 28.26 x 10 Step 1: So, V = 282.6 cubic centimeters or 282.6 cm 3. 9 Practice • • • • • • • • Finding the Volumes of Solids Directions: Use the formulae in this unit to answer the questions. 1. What is the volume of this rectangular solid? Volume = _____________________ 5'' 7'' 11'' 2. What is the volume of this cube? Volume = _____________________ 5'' 5'' 5'' 3. What is the volume of this cylinder? (Round to the nearest inch.) • 7'' (radius) Volume = _____________________ 14'' (height) 4. What is the volume of this cylinder? (Round to the nearest inch.) • 3'' (radius) Volume = _____________________ 20'' (height) 40 9 Practice • • • • • • • • Finding the Volumes of Solids 5. The sidewalk leading up to the school needs to be replaced. It has to be 4' wide, 100' long, and 1' deep. How much concrete should be poured? ______________________________ 6. What is the volume of this cube? Volume = _____________ 4.3’ 4.3' 4.3’ 4.3' 4.3’ 4.3' 7. How much liquid can this oil tank store? 14' diameter Volume = _____________ Gabrielʼs Fuel Oil 12' height 8. What is the volume of this cube? Volume = _____________ 3 ⁄2' 1 31⁄2' 31⁄2' 41 ▲ ● Pages 7 and 8 1. d 2. g 3. b 4. h 5. b 6. e 7. b 8. e 9. a 10. f 11. c 12. g 13. d 14. f Pages 12 and 13 1. b 2. f 3. a 4. f 5. b 6. g 7. d 8. e 9. b 10. e 11. c 12. h Page 17 1. 80° 2. 80° 3. 100° 4. 15° 5. g 6. f 7. 110° 8. 70° 9. 70° 10. 180° 11. 360° 12. 30° 13. 30° 14. 150° 15. 30° ■ • • • • • • • • • • • • • • • • • • • • • • Answer Key 6. parallelogram 7. 120 ft. 8. 36 ft. 9. 2.75 ft. 10. 7 ft. 11. 45 ft. 12. 14 ft. Pages 36 and 37 1. 120 ft.2 2. 48 ft.2 3. 400 yds.2 4. 110.25 in.2, 176 in.2 5. 40 ft.2 6. 14.625 ft.2 7. 12 ft.2 8. 6 in.2 9. 6 ft.2 10. 21.85 ft.2 11. 37.1 ft.2 12. 117 in.2 Pages 40 and 41 1. 385 in.3 2. 125 in.3 3. 2,154 in.3 4. 565.2 in.3 5. 400 ft.3 6. 79.507 ft.3 7. 1,846.32 ft.3 8. 427⁄8 ft.3 or 42.875 ft.3 Pages 42 and 43 1. 21 m; 9.5 m2 2. 12 m; 9 m2 3. 36 m; 81 m2 4. 162 m 5. 13.72 m; 4.64 m2 6. 155 cm 7. 25.6 m; 40.87 m2 8. 195 m 9. 84 ft.2 10. 336 ft.2 11. 4 quarts 12. 13.58 m2 13. 43,560 ft.2 14. 4,840 yards2 15. 1.10 acres Pages 20 and 21 1. radius 2. diameter 3. chord 4. circumference 5. 4 ft. 6. 6 in. 7. 9 ft. 8. 8 1⁄2 in. 9. 13⁄4 in. 10. 110 ft. 11. 20.41 miles 12. 5 1⁄2 yds. 13. 452.16 ft.2 14. 615.44 in.2 15. 314 ft.2 Page 25 1. acute 2. equilateral 3. right 4. isosceles 5. obtuse 6. scalene 7. acute 8. isosceles 9. acute 10. scalene 11. acute 12. equilateral Page 29 1. 60° 2. acute and scalene 3. 60° 4. acute and equilateral 5. D = 55° F = 55° 6. 50° 7. c = 2.5'' 8. b = 12' Pages 32 and 33 1. parallelogram 2. trapezoid 3. rhombus 4. rectangle 5. trapezoid 48 16. 3,780,000 pounds 17. A = 5,024 cm2 C = 251 cm 18. 16.75 minutes 19. r = 50 cm A = 7,850 cm2 C = 314 cm time = 20.93 min 20. r = 30 cm A = 2,826 cm2 C = 188.4 cm time = 12.56 min Pages 44 and 45 1. 32 cm2 = 1,024 cm2 2. P = 2(4s) = 16 cm 3. P = 4(4s) = 32 cm 4. A = 4(1 x w) = 16 cm2 5. A = 16(1 x w) = 64 cm2 6. 50° 7. Let side of square A = 1 cm Let the side of square B = 4 cm Area square A = 1 cm Area square B = 16 cm The area of square B is 16 times greater than the area of square A. 8. Area of rectangle = 70 cm x 30 cm = 2,100 cm2 2,100 cm2 + 600 cm2 = 2,700 cm2 30 x 2,700 cm2 = 81,000 cm2 of wood 9. Yes, they have the same area. Since you multiply the base and height, and these two parallelograms use the same numbers, so it doesn’t matter which is the base and which is the height.

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