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1. Physics is a field of study that governs
(a) How the planets orbit the sun.
(b) The rate at which blood flows through a person’s veins.
(c) How quickly a helium balloon will rise into the air.
(d) All of the above.
2. Who among the following is an example of a theoretical physicist?
(a) Archimedes, who measured the volume of water that was displaced after placing objects in a tub of water.
(b) Albert Einstein, who performed various thought experiments in his mind to arrive at his theories of relativity.
(c) Marie Curie, who, along with her husband, was credited with discovering radioactivity through a series of laboratory experiments.
(d) Benjamin Franklin, who determined, through various laboratory experiments, that electricity is the flow of microscopic charged particles.
3. Why are Isaac Newton conclusions on motion considered laws of physics?
(a) Newton himself declared them laws.
(b) Newton performed various thought experiments on motion.
(c) The formulas accompanying Newton’s laws have proved correct in experiments for years.
(d) Newton’s reputation alone made his scientific conclusions laws.
4. Which of the following is not considered a branch of physics?
(a) Thermodynamics
(b) Astronomy
(c) Geophysics
(d) Atomic physics
5. Analyzing the braking distance of a sports car would most likely utilize which field of physics?
(a) Molecular physics
(b) Quantum physics
(c) Fluid dynamics
(d) Mechanics

1. Who is considered to be the first true physicist and what did he do to deserve this recognition in scientific history?
2. Explain the difference between science and technology. Are the two fields related?
3. Provide two examples of scientific knowledge and a technological development that relies on that scientific knowledge.
4. What is the difference between the scientific method and the problem-solving method?
5. Why is it important to study physics? Provide a few examples of what an understanding of the physical world can do for you today and in your future.

Give the metric prefix for each value.
1. 1000
2. 0.01
3. 100
4. 0.1
5. 0.001
6. 10
7. 1,000,000
8. 0.000001

Give the metric symbol, or abbreviation, for each prefix.
1. Hecto
2. Kilo
3. Milli
4. Deci
5. Mega
6. Deka
7. Centi
8. Micro

Write the abbreviation for each quantity.
1. 135 Millimetres
2. 83 Dekagrams
3. 28 Kilolitres
4. 52 Centimetres
5. 49 Centigrams
6. 85 Milligrams
7. 75 Hectometres
8. 15 Decilitres

Write the SI unit for each abbreviation.
25. 24 m
26. 185 L
27. 59 g
28. 125 kg
29. 27 mm
30. 25 dL
31. 45 dam
32. 27 mg
33. 26 Mm
34. 275 mg
35. The basic metric unit of length is _____.
36. The basic unit of mass is _____.
37. Two common metric units of volume are _____ and _____.
38. The basic unit for electric current is _____.
39. The basic metric unit for time is _____.
40. The common metric unit for power is _____.

Write each number in scientific notation.
1. 326
2. 798
3. 2650
4. 14,500
5. 826.4
6. 24.97
7. 0.00413
8. 0.00053
9. 6.43
10. 482,300
11. 0.000065
12. 0.00224
13. 540,000
14. 1,400,000
15. 0.0000075
16. 0.0000009
17. 0.00000005
18. 3,500,000,000
19. 732,000,000,000,000,000
20. 0.000000000000000618

Write each number in decimal form.
1. 8.62 x 104
2. 8.67 x 102
3. 6.31 x 10–4
4. 5.41 x 103
5. 7.68 x 10–1
6. 9.94 x 101
7. 7.77 x 108
8. 4.19 x 10–6
9. 6.93 x 101
10. 3.78 x 10–2
11. 9.61 x 104
12. 7.33 x 103
13. 1.4 x 100
14. 9.6 x 10–5
15. 8.4 x 10–6
16. 9 x 108
17. 7 x 1011
18. 4.05 x 100
19. 7.2 x 10–7
20. 8 x 10–9
21. 4.5 x 1012
22. 1.5 x 1011
23. 5.5 x 10–11
24. 8.72 x 10–10

Which unit is longer?
1. 1 metre or 1 centimetre
2. 1 metre or 1 millimetre
3. 1 metre or 1 kilometre
4. 1 centimetre or 1 millimetre
5. 1 centimetre or 1 kilometre
6. 1 millimetre or 1 kilometre

Which metric unit (km, m, cm, or mm) would you use to measure the following?
1. Length of a wrench
2. Thickness of a saw blade
3. Height of a barn
4. Width of a table
5. Thickness of a hypodermic needle
6. Distance around an automobile racing track
7. Distance between New York and Miami
8. Length of a hurdle race
9. Thread size on a pipe
10. Width of a house lot

Fill in each blank with the most reasonable metric unit (km, m, cm, or mm).
1. Your car is about 6 _____ long.
2. Your pencil is about 20 _____ long.
3. The distance between New York and San Francisco is about 4200 _____.
4. Your pencil is about 7 _____ thick.
5. The ceiling in my bedroom is about 240 _____ high.
6. The length of a football field is about 90 _____.
7. A jet plane usually cruises at an altitude of 9 _____.
8. A standard film size for cameras is 35 _____.
9. The diameter of my car tire is about 60 _____.
10. The zipper on my jacket is about 70 _____ long.
11. Juan drives 9 _____ to school each day.
12. Jacob, our basketball center, is 203 _____ tall.
13. The width of your hand is about 80 _____.
14. A handsaw is about 70 _____ long.
15. A newborn baby is usually about 45 _____ long.
16. The standard metric piece of plywood is 120 _____ wide and 240 _____ long.

Fill in each blank.
1. 1 km = _____ m
2. 1 mm = _____ m
3. 1 m = _____ cm
4. 1 m = _____ hm
5. 1 dm = _____ m
6. 1 dam =_____ m
7. 1 m = _____ mm
8. 1 m = _____ dm
9. 1 hm = _____ m
10. 1 cm = _____ m
11. 1 m = _____ km
12. 1 m = _____ dam
13. 1 cm = _____ mm

1. Change 250 m to cm.
2. Change 250 m to km.
3. Change 546 mm to cm.
4. Change 178 km to m.
5. Change 35 dm to dam.
6. Change 830 cm to m.
7. Change 75 hm to km.
8. Change 375 cm to mm.
9. Change 7.5 mm to μm.
10. Change 4 m to μm.
11. The wheelbase of a certain automobile is 108 in. long. Find its length.
(a) In feet.
(b) In yards.
12. Change 43,296 ft.
(a) To miles.
(b) To yards.
13. Change 6.25 mi.
(a) To yards.
(b) To feet.

1. The length of a connecting rod is 7 in. What is its length in centimetres?
2. The distance between two cities is 256 mi. Find this distance in kilometres.
3. Change 5.94 m to feet.
4. Change 7.1 cm to inches.
5. Change 1.2 in. to centimetres.
6. The turning radius of an auto is 20 ft. What is this distance in metres?
7. Would a wrench with an opening of 25 mm be larger or smaller than a 1-in. wrench?

How many reamers, each 20 cm long, can be cut from a bar 6 ft long, allowing 3 mm for each saw cut?

If 214 pieces each 47 cm long are to be turned from 1/4-in. round steel stock with 1/8 in of waste allowed on each piece, what length (in metres) of stock is required?

Find the area of each figure.
1.

Find the area of each figure. 1.  .:. 2.

2.

Find the area of each figure. 1.  .:. 2.

3.

Find the area of each figure. 1.  .:. 2.

4.

Find the area of each figure. 1.  .:. 2.

5. Find the cross-sectional area of the I-beam.

Find the area of each figure. 1.  .:. 2.

6. Find the largest cross-sectional area of the figure.

Find the area of each figure. 1.  .:. 2.

7. Find the volume in eachfigure.
Which unit is larger?
11. 1 litre or 1 centilitre
12. 1 millilitre or 1 kilolitre
13. 1 cubic millimetre or 1 cubic centimetre
14. 1 cm3 or 1 m3
15. 1 square kilometre or 1 hectare
16. 1 mm2 or 1 dm2

Which metric unit (m3, L, mL, m2, cm2, ha) would you use to measure the following?
1. Oil in your car’s crankcase.
2. Water in a bathtub.
3. Floor space in a house.
4. Cross section of a piston.
5. Storage space in a miniwarehouse.
6. Coffee in an office coffeepot.
7. Size of a field of corn.
8. Page size of a newspaper.
9. A dose of cough syrup.
10. Size of a cattle ranch.
11. Cargo space in a truck.
12. Gasoline in your car’s gas tank.
13. Piston displacement of an engine.
14. Paint needed to paint a house.
15. Dose of eye drops.
16. Size of a plot of timber.

Fill in the blank with the most reasonable metric unit (m3, L, mL, m2, cm2, ha).
1. Go to the store and buy 4 _____ of root beer for the party.
2. I drank 200 _____ of orange juice for breakfast.
3. Craig bought a 30-_____ tarpaulin for his truck.
4. The cross section of a log is 3200 _____.
5. A farmer’s gasoline storage tank holds 4000 _____.
6. Our city water tower holds 500 _____ of water.
7. Brian planted 60 _____ of soybeans this year.
8. David needs some copper tubing with a cross section of 3 _____.
9. Paula ordered 15 _____ of concrete for her new driveway.
10. Barbara heats 420 _____ of living space in her house.
11. Joyce’s house has 210 _____ of floor space.
12. Kurt mows 5 _____ of grass each week.
13. Amy is told by her doctor to drink 2 _____ of water each day.
14. My favorite coffee cup holds 225 _____ of coffee.

Fill in each blank.
1. 1 L = _____ mL
2. 1 kL = _____ L
3. 1 L = _____ daL
4. 1 L = _____ kL
5. 1 L = _____ hL
6. 1 L = _____ dL
7. 1 daL = _____ L
8. 1 mL = _____ L
9. 1 mL = _____ cm3
10. 1 L = _____ cm3
11. 1 m3 = _____ cm3
12. 1 cm3 = _____ mL
13. 1 cm3 = _____ L
14. 1 dm3 = _____ L
15. 1 m2 = _____ cm2
16. 1 km2 = _____ m2
17. 1 cm2 = _____ mm2
18. 1 mm2 = _____ m2
19. 1 dm2 = _____ m2
20. 1 ha = _____ m2
21. 1 km2 = _____ ha
22. 1 ha = _____ km2

1. Change 7500 mL to L.
2. Change 0.85 L to mL.
3. Change 1.6 L to mL.
4. Change 9 mL to L.
5. Change 275 cm3 to mm3.
6. Change 5 m3 to cm3.
7. Change 4 m3 to mm3.
8. Change 520 mm3 to cm3.
9. Change 275 cm3 to mL.
10. Change 125 cm3 to L.
11. Change 1 m3 to L.
12. Change 150 mm3 to L.
13. Change 7.5 L to cm3.
14. Change 450 L to m3.
15. Change 5000 mm2 to cm2.
16. Change 1.75 km2 to m2.
17. Change 5 m2 to cm2.
18. Change 250 cm2 to mm2.
19. Change 4 x 108 m2 to km2.
20. Change 5 x 107 cm2 to m2.
21. Change 5 yd2 to ft2.
22. How many m2 are in 225 ft2?
23. Change 15 ft2 to cm2.

1. How many ft2 are in a rectangle 15 m long and 12 m wide?
2. Change 108 in2 to ft2.
3. How many in2 are in 51 cm2?
4. How many in2 are in a square 11 yd on a side?
5. How many m2 are in a doorway whose area is 20 ft2?
6. Change 19 yd3 to ft3.
7. How many in3 are in 29 cm3?
8. How many yd3 are in 23 m3? 100. How many cm3 are in 88 in3?
9. Change 8 ft3 to in3.
10. How many in3 are in 12 m3?

1. The volume of a casting is 38 in3. What is its volume in cm3?
2. How many castings of 14 cm3 can be made from a 12-ft3 block of steel?
3. Find the lateral surface area of the figure in Problem 9.
4. Find the lateral surface area of the figure in Problem 10.
5. Find the total surface area of the figure in Problem 9.
6. Find the total surface area of the figure in Problem 10.
7. How many mL of water would the figure in Problem 9 hold?
8. How many mL of water would the figure in Problem 8 hold?

Which unit is larger?
1. 1 gram or 1 centigram
2. 1 gram or 1 milligram
3. 1 gram or 1 kilogram
4. 1 centigram or 1 milligram
5. 1 centigram or 1 kilogram
6. 1 milligram or 1 kilogram

Which metric unit (kg, g, mg, or metric ton) would you use to measure the following?
1. Your mass
2. An aspirin
3. A bag of lawn fertilizer
4. A bar of hand soap
5. A trainload of grain
6. A sewing needle
7. A small can of corn
8. A channel catfish
9. A vitamin capsule
10. A car

Fill in each blank with the most reasonable metric unit (kg, g, mg, or metric ton).
1. A newborn’s mass is about 3 _____.
2. An elevator in a local department store has a load limit of 2000 _____.
3. Margie’s diet calls for 250 _____ of meat.
4. A 200-car train carries 11,000 _____ of soybeans.
5. A truckload shipment of copper pipe has a mass of 900 _____.
6. A carrot has a mass of 75 _____.
7. A candy recipe calls for 175 _____ of chocolate.
8. My father has a mass of 70 _____.
9. A pencil has a mass of 10 _____.

1. Postage rates for letters would be based on the _____.
2. A heavyweight boxing champion has a mass of 93 _____.
3. A nickel has a mass of 5 _____.
4. My favorite spaghetti recipe calls for 1 _____ of ground beef.
5. My favorite spaghetti recipe calls for 150 _____ of tomato paste.
6. Our local grain elevator shipped 10,000 _____ of wheat last year.
7. A slice of bread has a mass of about 25 _____.
8. I bought a 5-_____ bag of potatoes at the store today.
9. My grandmother takes 250-_____ capsules for her arthritis.

Fill in each blank.
1. 1 kg = _____ g
2. 1 mg = _____ g
3. 1 g = _____ cg
4. 1 g = _____ hg
5. 1 dg = _____ g
6. 1 dag = _____ g
7. 1 g = _____ mg
8. 1 g = _____ dg
9. 1 hg = _____ g
10. 1 cg = _____ g
11. 1 g = _____ kg
12. 1 g = _____ dag
13. 1 g = _____ μg
14. 1 mg = _____ μg

1. Change 575 g to mg.
2. Change 575 g to kg.
3. Change 650 mg to g.
4. Change 375 kg to g.
5. Change 50 dg to g.
6. Change 485 dag to dg.
7. Change 30 kg to mg.
8. Change 4 metric tons to kg.
9. Change 25 hg to kg.
10. Change 58 mg to g.
11. Change 400 mg to mg.
12. Change 30,000 kg to metric tons.
13. What is the mass of 750 mL of water?
14. What is the mass of 1 m3 of water?

1. The weight of a car is 3500 lb. Find its weight in newtons.
2. A certain bridge is designed to support 150,000 lb. Find the maximum weight that it will support in newtons.
3. Jose weighs 200 lb. What is his weight in newtons?
4. Change 80 lb to newtons.
5. Change 2000 N to pounds.
6. Change 2000 lb to newtons.
7. Change 120 oz to pounds.
8. Change 3.5 lb to ounces.
9. Change 10 N to ounces.
10. Change 25 oz to newtons.
11. Find the metric weight of a 94-lb bag of cement.
12. What is the weight in newtons of 500 blocks if each weighs 3 lb?

Fill in each blank.
1. The basic metric unit of time is _____. Its abbreviation is _____.
2. The basic metric unit of mass is _____. Its abbreviation is _____.
3. The common metric unit of weight is _____. Its abbreviation is _____.

Which is larger?
1. 1 second or 1 millisecond
2. 1 millisecond or 1 nanosecond
3. 1 ps or 1 μs
4. 1 ms or 1 μs

Write the abbreviation for each unit.
1. 8.6 microseconds
2. 45 nanoseconds
3. 75 picoseconds
4. Change 345 μs to s.
5. Change 1 h 25 min to min.
6. Change 4 h 25 min 15 s to s.
7. Change 7 x 106 s to h.
8. Change 4 s to ns.
9. Change 1 h to ps.

Determine the accuracy (the number of significant digits) of each measurement.
1. 536 ft
2. 307.3 mi
3. 5007 m
4. 5.00 cm
5. 0.0070 in.
6. 6.010 cm
7. 8400 km
8. 3000 ft
9. 187.40 m
10. 500 g

Determine the accuracy (the number of significant digits) of each measurement.
1. 0.00700 in.
2. 10.30 cm
3. 376.52 m
4. 3.05 mi
5. 4087 kg
6. 35.00 mm
7. 0.0160 in.
8. 370 lb
9. 4000 N
10. 5010 ft3

Determine the accuracy (the number of significant digits) of each measurement.
1. 7 N
2. 32,000 tons
3. 70.00 m2
4. 0.007 m
5. 2.4 x 103 kg
6. 1.20 x 10–5 ms
7. 3.00 x 10–4 kg
8. 4.0 x 106 ft
9. 5.106 x 107 kg
10. 1 x 10–9 m

Determine the precision of each measurement.
1. 536 ft
2. 307.3 mi
3. 5007 m
4. 5.00 cm
5. 0.0070 in.
6. 6.010 cm
7. 8400 km
8. 3000 ft
9. 187.40 m
10. 500 g

1. 0.00700 in.
2. 10.30 cm
3. 376.52 m
4. 3.05 mi
5. 4087 kg
6. 35.00 mm
7. 0.0160 in.
8. 370 lb
9. 4000 N
10. 5010 ft3

Determine the precision of each measurement.
1. 7 N
2. 32,000 tons
3. 70.00 m2
4. 0.007 m
5. 2.4 x 103 kg
6. 1.20 x 10–5 ms
7. 3.00 x 10–4 kg
8. 4.0 x 106 ft
9. 5.106 x 107 kg
10. 1 x 10–9 m

In each set of the measurements, find the measurement that is
(a) The most accurate
(b) The most precise.
1. 15.7 in.; 0.018 in.; 0.07 in.
2. 368 ft; 600 ft; 180 ft
3. 0.734 cm; 0.65 cm; 16.01 cm
4. 3.85 m; 8.90 m; 7.00 m
5. 0.0350 s; 0.025 s; 0.00040 s; 0.051 s
6. 125.00 g; 8.50 g; 9.000 g; 0.05 g
7. L; 350 L; 27.6 L; 4.75 L
8. 8.4 m; 15 m; 180 m; 0.40 m
9. 500 N; 10,000 N; 500,000 N; 50 N
10. 7.5 ms; 14.2 ms; 10.5 ms; 120.0 ms

In each set of measurements, find the measurement that is
(a) The least accurate
(b) The least precise.
1. 16.4 in.; 0.075 in.; 0.05 in.
2. 475 ft; 300 ft; 360 ft
3. 27.5 m; 0.65 m; 12.02 m
4. 5.7 kg; 120 kg; 0.025 kg
5. 0.0250 g; 0.015 g; 0.00005 g; 0.75 g
6. 185.0 m; 6.75 m; 5.000 m; 0.09 m
7. 45,000 N; 250 N; 16.8 N; 0.25 N; 3 N
8. 2.50 kg; 42.0 kg; 15 kg; 0.500 kg
9. 2000 kg; 10,000 kg; 400,000 kg; 20 kg
10. 80 ft; 250 ft; 12,550 ft; 2600 ft

Use the rules for addition of measurements to add each set of measurements.
1.
3847 ft
5800 ft
4520 ft
2.
8560 m
84,000 m
18,476 m
12,500 m
3.
42.8 cm
16.48 cm
1.497 cm
12.8 cm
9.69 cm
4.
0.456 g
0.93 g
0.402 g
0.079 g
0.964 g

5. 39,000 N; 19,600 N; 8470 N; 2500 N
6. 6800 ft; 2760 ft; 4000 ft; 2000 ft
7. 467 m; 970 cm; 1200 cm; 1352 cm; 300 m
8. 36.8 m; 147.5 cm; 1.967 m; 125.0 m; 98.3 cm
9. 12 s; 1.004 s; 0.040 s; 3.9 s; 0.87 s
10. 160,000 N; 84,200 N; 4300 N; 239,000 N; 17,450 N

Use the rules for subtraction of measurements to subtract each second measurement from the first.
1.
2876 kg
2400 kg
2.
14.73 m
9.378 m
3.
45.585 g
4.6 g
4.
34,500 kg
9,500 kg
5. 4200 km – 975 km
6. 64.73 g – 9.4936 g
7. 1,600,000 kg – 685,000 kg
8. 170 mm – 10.2 cm
9. 3.00 m – 260 cm
10. 1.40 ms – 0.708 ms

Use the rules for multiplication of measurements to multiply each set of measurements.
1. (125 m)(39 m)
2. (470 ft)(1200 ft)
3. (1637 km)(857 km)
4. (9100 m)(600 m)
5. (18.70 m)(39.45 m)
6. (565 cm)(180 cm)
7. (14.5 cm)(18.7 cm)(20.5 cm)
8. (0.046 m)(0.0317 m)(0.0437 m)
9. (450 in.) (315 in.) (205 in.)
10. (18.7 kg)(217 m)

Use the rules for division of measurements to divide.
1. 360 ft3 ÷ 12 ft2
2. 125 m2 ÷ 3.0 m
3. 275 cm2 ÷ 90.0 cm
4. 185 mi ÷ 4.5 h
5. 348 km
4.6 h
6. 2700 m3
900 m2
7. 8800 ft
8.5 h
8. 4960 ft
2.95 s

Use the rules for multiplication and division of measurements to find the value of each of the following.
1. (18 ft) (290 lb)/4.6 s
2. (18.5 kg) (4.65 m)/19.5 s
3. 4500 mi/12.3 h
4. 48.9 kg (1.5 m) (3.25 m)
5. (48.7 m) (68.5 m)/18.4 m)/(35.5 m) (40.0 m)
6. ½(270 kg) (16.4 m/s)2
7. (85.7 kg) (25.7 m/s)2/12.5 m
8. (45.2 kg) (13.7 m)/(2.65 s)2
9. 4/3π (13.5 m)3
10. 140 g/(3.4 cm) (2.8 cm)/(5.6 cm)
11. (213 m) (65.3 m) – (175 m)(44.5 m)
12. (4.5 ft) (7.2 ft) (12.4 ft) + (5.42 ft)3
13. (125 ft) (295 ft)/44.7 ft + (215 ft)3/(68.8 ft) (12.4 ft) + (454 ft)3/(75.5 ft)2
14. (12.5 m) (46.75 m) + (6.76 m)3/4910 m + (41.5 m)(21 m) (28.8 m)/31.7 m


Give the metric prefix for each value:
1. 1000
2. 0.001
Give the metric symbol, or abbreviation, for each prefix:
3. Micro
4. Mega
Write the abbreviation for each quantity:
5. 45 milligrams
6. 138 centimetres
Which is larger?
7. 1 L or 1 mL
8. 1 kg or 1 mg
9. 1 L or 1 m3

Fill in each blank (round to three significant digits when necessary):
1. 250 m = _____ km
2. 850 mL = _____ L
3. 5.4 kg = _____ g
4. 0.55 s = _____ μs
5. 25 kg = _____ g
6. 75 μs = _____ ns
7. 275 cm2 = _____ mm2
8. 350 cm2 = _____ m2
9. 0.15 m3 = _____ cm3
10. 500 cm3 = _____ mL
1. 150 lb _ _____ kg
12. 36 ft = _____ m
13. 250 cm = _____ in.
14. 150 in2 = _____ cm2
15. 24 yd2 = _____ ft2
116. 6 m3 = _____ ft3
17. 16 lb = _____ N
18. 15,600 s = _____ h _____ min

Determine the accuracy (the number of significant digits) in each measurement:
1. 5.08 kg
2. 20,570 lb
3. 0.060 cm
4. 2.00 x 10–4 s

Determine the precision of each measurement:
1. 30.6 ft
2. 0.0500 s
3. 18,000 mi
4. 4 x 105 N

For each set of measurements, find the measurement that is
(a) The most accurate.
(b) The least accurate.
(c) The most precise.
(d) The least precise.
1. 12.00 m; 0.150 m; 2600 m; 0.008 m
2. 208 L; 18,050 L; 21.5 L; 0.75 L

Use the rules of measurements to add the following measurements:
1. 0.0250 s; 0.075 s; 0.00080 s; 0.024 s
2. 2100 N; 36,800 N; 24,000 N; 14.5 N; 470 N
Use the rules for multiplication and division of measurements to find the value of each of the following:
3. (450 cm)(18.5 cm)(215 cm)
4. 1480 m3/9.6 m
5. (25.0 kg) (1.20 m/s)2 3.70 m
6. Find the area of a rectangle 4.50 m long and 2.20 m wide.
7. Find the volume of a rectangular box 9.0 cm long, 6.0 cm wide, and 13 cm high.

What are the basic metric units for length, mass, and time?
(a) Foot, pound, hour
(b) Newton, litre, second
(c) Metre, kilogram, second
(d) Mile, ton, day

1. When a value is multiplied or divided by 1, the value is
(a) Increased.
(b) Unchanged.
(c) Decreased.
(d) None of the above.
2. The lateral surface area of a solid is
(a) Always equal to total surface area.
(b) Never equal to total surface area.
(c) Usually equal to total surface area.
(d) Rarely equal to total surface area.
3. Accuracy is
(a) The same as precision.
(b) The smallest unit with which a measurement is made.
(c) The number of significant digits.
(d) All of the above.
4. When multiplying or dividing two or more measurements, the units
(a) Must be the same.
(b) Must be different.
(c) Can be different.

Cite three examples of problems that would arise in the construction of a home by workers using different systems of measurement.

1. Why is the metric system preferred worldwide to the U.S. system of measurement?
2. List a very large and a very small measurement that could be usefully written in scientific notation.
3. When using conversion factors, can units be treated like other algebraic quantities?
4. What is the meaning of cross-sectional area?
5. Can a brick have more than one cross-sectional area?
6. What is the fundamental metric unit for land area?
7. Which is larger, a litre or a quart?

List three things that might conveniently be measured in millilitres.

1. How do weight and mass differ?
2. What is the basic metric unit of weight?
3. A microsecond is one-_____ of a second.
4. Why must we concern ourselves with significant digits?
5. Can the sum or difference of two measurements ever be more precise than the least precise measurement?
6. When rounding the product or quotient of two measurements, is it necessary to consider significant digits?

You run a landscaping business and know that you want to charge $50.00 to mow a person’s lawn whose property is 100 ft x 200 ft. If the house dimensions take up a 35.0 ft x 80.0 ft area, how much are you charging per square yard?

A room that measures 10.0 ft wide, 32.0 ft long, and 8.00 ft high needs a certain amount of air pumped into it per minute to keep the air quality up to regulations. If the room needs completely new air every 20.0 minutes, what is the volume of air per second that is being pumped into the room?

Instead of using a solid iron beam, structural engineers and contractors use I-beams to save materials and money. How many I-beams can be molded from the same amount of iron contained in the solid iron beam as shown in Fig.2.12?
Instead of using a solid iron beam, structural engineers and
A shipping specialist at a craft store needs to pack Styrofoam balls of radius 4.00 in. into a 1.40 ft x 2.80 ft x 1.40 ft rectangular cardboard container. What is the maximum number of balls that can fit in the container? Spherical balls have spaces around them when packed in rectangular containers.

A crane needs to lift a spool of fine steel cable to the top of a bridge deck. The type of steel in the cable has a density of 7750 kg/m3. The maximum lifting mass of the crane is 43,400 kg.
(a) Given the dimensions of the spool in Fig. 2.13, find the volume of the spool.

A crane needs to lift a spool of fine steel

(b) Can the crane safely lift thespool?
Solve each formula for the quantity given.
1. v = s/t for s
2. a = v/t for v
3. w = mg for m
4. F = ma for a
5. E = IR for R
6. V = lwh for w
7. Ep = mgh for g
8. Ep = mgh for h
9. v2 = 2gh for h
10. XL = 2πfL for f

Solve each formula for the quantity given.
1. P = W/t for W
2. p = F/A for F
3. P = W/t for t
4. p = F/A for A
5. Ek = ½ mv2 for m
6. Ek = ½ mv2 for v2
7. W = FS for s
8. vf = vi + at for a
9. V = E – Ir for I
10. v2 = v1 + at for t

Solve each formula for the quantity given.
1. R = π/P for P
2. R = kL/d2 for L
3. F = 9/3C + 32 for C
4. C = 5/9 (F – 32) for F
5. XC = I/2πfC for f
6. R = ρL/A for L
7. RT = R1 + R2 + R3 + R4, for R3
8. Q1 = P(Q2 – Q1, for Q2
9. IS/IP = NP/NS for IP
10. Vp/Vs = NP/NS for NS

Solve each formula for the quantity given.
1. vavg = ½ (vf + vi) for vi
2. 2a (s – si) = v2 – v2i for a
3. 2a (s – si) = v2 – v2i for s
4. Ft = m (V2 – V1) for V1
5. Q = I2Rt/J for R
6. x = xi + vit + ½ at2 for xi
7. A = πr2 for r, where r is a radius
8. V = πr2h for r, where r is a radius
9. R = kL/d2 for d, where d is a diameter
10. V = 1/3 πr2h for r, where d is a radius
11. Q = I2Rt/J for I
12. F = mv2/r for v

For each formula,
(a) Solve for the indicated letter and then
(b) Substitute the given data to find the value of the indicated letter.

For each formula, (a) Solve for the indicated letter and

Follow the rules of calculations withmeasurements.
For each formula, (a) solve for the indicated letter and then (b) substitute the given data to find the value of the indicated letter.

For each formula, (a) solve for the indicated letter and then

Follow the rules of calculations withmeasurements.
Use the problem-solving method to work each problem. (Here, as throughout the text, follow the rules for calculations with measurements.)
1. Find the volume of the box in Fig. 2.3.

Use the problem-solving method to work each problem. (Here, as

2. Find the volume of a cylinder whose height is 7.50 in. and diameter is 4.20 in. (Fig. 2.4).

Use the problem-solving method to work each problem. (Here, as

3. Find the volume of a cone whose height is 9.30 cm if the radius of the base is 5.40 cm (Fig. 2.5).

Use the problem-solving method to work each problem. (Here, as

The cylinder in an engine of a road grader as shown in Fig. 2.6 is 11.40 cm in diameter and 24.00 cm high. Use Fig. 2.6 for Problems 4 through 6.

Use the problem-solving method to work each problem. (Here, as

4. Find the volume of the cylinder.
5. Find the cross-sectional area of the cylinder.
6. Find the lateral surface area of the cylinder.
7. Find the total volume of the building shown in Fig. 2.7.

Use the problem-solving method to work each problem. (Here, as

8. Find the cross-sectional area of the concrete retaining wall shown in Fig. 2.8.

Use the problem-solving method to work each problem. (Here, as

9. Find the volume of a rectangular storage facility 9.00 ft by 12.0 ft by 8.00 ft.
10. Find the cross-sectional area of a piston head with a diameter of 3.25cm.

1. Find the area of a right triangle that has legs of 4.00 cm and 6.00 cm.

2. Find the length of the hypotenuse of the right triangle in Problem 11.

3. Find the cross-sectional area of a pipe with outer diameter 3.50 cm and inner diameter

3.20 cm.

4. Find the volume of a spherical water tank with radius 8.00 m.

5. The area of a rectangular parking lot is 900 m2. If the length is 25.0 m, what is the width?

6. The volume of a rectangular crate is 192 ft3. If the length is 8.00 ft and the width is 4.00 ft, what is the height?

7. Find the volume of a brake cylinder whose diameter is 4.00 cm and whose length is 4.20 cm.

8. Find the volume of a tractor engine cylinder whose radius is 3.90 cm and whose length is 8.00 cm.

9. A cylindrical silo has a circumference of 29.5 m. Find its diameter.

10. If the silo in Problem 19 has a capacity of 1000 m3, what is its height?

1. A wheel 30.0 cm in diameter moving along level ground made 145 complete rotations. How many metres did the wheel travel?
2. The side of the silo in Problems 19 and 20 needs to be painted. If each litre of paint covers 5.0 m2, how many litres of paint will be needed? (Round up to the nearest litre.)
3. You are asked to design a cylindrical water tank that holds gal with radius 18.0 ft. Find its height. (1 ft3 = 7.50 gal)
4. If the height of the water tank in Problem 23 were 42.0 ft, what would be its radius?
5. A ceiling is 12.0 ft by 15.0 ft. How many suspension panels 1.00 ft by 3.00 ft are needed to cover the ceiling?
6. Find the cross-sectional area of the dovetail slide shown in Fig.2.9.
1. A wheel 30.0 cm in diameter moving along level
1. Find the volume of the storage bin shown in Fig. 2.10.

1. Find the volume of the storage bin shown in

2. The maximum cross-sectional area of a spherical propane storage tank is 3.05 m2. Will it fit into a 2.00-m-wide trailer?
3. How many cubic yards of concrete are needed to pour a patio 12.0 ft x 20.0 ft and 6.00 in. thick?
4. What length of sidewalk 4.00 in. thick and 4.00 ft wide could be poured with 2.00 yd3 of concrete? Find the volume of each figure.
5.

1. Find the volume of the storage bin shown in

6.

1. Find the volume of the storage bin shown in

Inside diameter: 20.0 cm
Outside diameter: 50.0cm
1. Solve F = ma for (a) m and (b) a.
2. Solve v = √2gh for h.
3. Solve s = ½ (vf + vi) for vf.
4. Solve Ek = ½ mv2 for v.

1. Given P = a + b + c, with P = 36 ft, a = 12 ft, and c = 6 ft, find b.
2. Given A = (a + b/2)h, with A = 210 m2, b – 16.0 m, and h = 15.0, find a.
3. Given A = πr2, if A = 15.0 m2, find r.
4. Given A = 1/2bh, if b = 12.2 cm and h = 20.0 cm, what is A?

1. A cone has a volume of 314 cm3 and radius of 5.00 cm. What is its height?
2. A right triangle has a side of 41.2 mm and a side of 9.80 mm. Find the length of the hypotenuse.
3. Given a cylinder with a radius of 7.20 cm and a height of 13.4 cm, find the lateral surface area.
4. A rectangle has a perimeter of 40.0 cm. One side has a length of 14.0 cm. What is the length of an adjacent side?

1. The formula for the volume of a cylinder is V = πr2h. If V = 2100 m3 and h = 17.0m, find r.
2. The formula for the area of a triangle is A = ½bh. If b = 12.3 m and A = 88.6 m2, find h.
3. Find the volume of the lead sleeve with the cored hole in Fig. 2.11.

1. The formula for the volume of a cylinder is

4. A rectangular plot of land measures 40.0 m by 120 m with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer. What is the area of the remainingplot?
1. A formula is
(a) The amount of each value needed.
(b) A solution for problems.
(c) An equation usually expressed in letters and numbers.
2. Subscripts are
(a) The same as exponents.
(b) Used to shorten what must be written.
(c) Used to make a problem look hard.
3. A working equation
(a) Is derived from the basic equation.
(b) Is totally different from the basic equation.
(c) Comes before the basic equation in the problem.
(d) None of the above.
4. Cite two examples in industry in which formulas are used.
5. How are subscripts used in measurement?

1. Why is reading the problem carefully the most important step in problem solving?
2. How can making a sketch help in problem solving?
3. What do we call the relationship between data that are given and what we are asked to find?
4. How is a working equation different from a basic equation?
5. How can analysis of the units in a problem assist in solving the problem?
6. How can making an estimate of your answer assist in the correct solution of problems?

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