1. No category

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
▲
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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°
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• • • • • • • • • • • • • • • • • • • • • • 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.