Chapter Review Problems
Unless instructed otherwise, use up to 2 decimal places for final answers. Assume π = 3.14.
Unit 22.1 Length, area, and volume: Applications
1. If the ground is level, at what angle should the wall of a building be in relation to the ground?
2. A square is a type of rectangle. (T or F)
True
For Problems 3–5 find the perimeter. Some dimensions are intentionally not shown.
3.
4.
5.
10 ft
10 ft
5 ft
12 ft
20 ft
20 in.
23.32 in.
12 in.
10 ft + 12 ft + 13 ft + 20 ft + 20 ft = 75 ft
20 ft
15 ft
10 ft
13 ft
20 ft
90°
5 ft
23.32 in. + 12 in. + 20 in. = 55.32 in.
5 ft
10 ft + 20 ft + 5 ft + 10 ft + 15 ft +
10 ft + 5 ft + 20 ft + 5 ft + 5 ft + 10 ft +
5 ft = 120 ft
6. A farmer wants to fence a field measuring 660 ft × 330 ft. How many feet of fencing are required?
P = 2(L + W) = 2(660 ft + 330 ft) = 2(990 ft) = 1,980 ft
7. Write in order from smallest to largest: diameter (d), radius (r), circumference (c).
r, d, c. Diameter is twice the radius; circumference is about 3.14 times the diameter.
8. A large earthmoving machine has tires with a diameter of 9 ft. How far does the machine travel for each revolution of
the wheels? C = πd ≈ 3.14(9 ft) ≈ 28.26 ft
9. You see a large redwood tree. You run a tape measure around the tree and get a measurement of 44 ft. How thick is
the tree?
44 ft ≈ 14.01 ft
d = πc ≈ 3.14
For Problems 10 and 11, determine the area of the shaded region.
10.
38 in.
Rectangle: A = LW = (38 in.)(30 in.)
Triangle: A = 21 bh = 12 (7 in.)(30 in.)
Total area
30 in.
1,140 in.2
+ 105 in.2
1,245 sq in.
45 in.
11.
15 in.
Entire circle: A = πr2 ≈ 3.14(15 in.)(15 in.)
Inner circle: A = πr2 ≈ 3.14(3 in.)(3 in.)
Net area
3 in.
706.50 in.2
- 28.26 in.2
678.24 sq in.
12. A home has measurements as shown. Dimensions are in feet. What is the square footage of the home?
20
25
15
5
30
30
Large rectangle: A = LW = (60 ft)(30 ft) =
Missing rectangle: A = LW = (15 ft)(5 ft) =
Rectangle at bottom: A = LW = (30 ft)(5 ft) =
Total square footage
5
30
446
Chapter 22
Measurements: Real-World Applications
1,800
- 75
+ 150
1,875
ft2
ft2
ft2
sq ft
13. From a fire observation tower, a forest ranger can see a distance of 50 miles in all directions. How many square miles
can be observed from the tower?
A = πr2 ≈ 3.14(50 mi)(50 mi) ≈ 7,850 sq mi
For Problems 14–16, find the volume of the object.
14.
15 in.
15 in.
V = LWH = (15 in.)(15 in.)(15 in.) = 3,375 cu in.
15 in.
15.
10 ft
10 ft
20 ft
Entire cube: V = LWH = (25 ft)(15 ft)(20 ft) =
Missing portion: V = LWH = (10 ft)(15 ft)(10 ft) =
Net volume
7,500 ft3
-1,500 ft3
6,000 cu ft
15 ft
25 ft
16.
h = 10 in.
V = πr2h ≈ 3.14(5 in.)(5 in.)(10 in.) ≈ 785 cu in.
r = 5 in.
17. A theater is 40 ft wide, 90 ft deep, and 18 ft high. Allowing 250 cubic feet of airspace per patron, what is the maximum number of tickets that should be sold for each movie?
V = LWH = (90 ft)(40 ft)(18 ft) = 64,800 cu ft
64,800 ÷ 250 = 259.20 = 259 tickets
18. An underground gasoline storage tank has a diameter of 28 ft and is 15 ft tall. Find the volume.
V = πr2h ≈ 3.14(14 ft)(14 ft)(15 ft) ≈ 9,231.60 cu ft
19. If all the gold in the world were gathered together, it would reportedly form a cube 18 yards on a side. Find the volume of the world’s gold (in cubic yards).
V = LWH = (18 yd)(18 yd)(18 yd) = 5,832 cu yd
Unit 22.2 Unit costs and converting measurements (U.S. to U.S.)
20. You have a choice of buying a 68-oz bottle of soda pop for $1.19 or a six-pack of 12-oz cans for $1.49. Which is
cheaper per ounce? Hint: Figure the cost per ounce in cents not dollars.
Cost per ounce =
Cost
= $1.19 = $0.0175 per oz = 1.75¢ per oz
Number of ounces 68 oz
Six-pack: Cost per ounce =
Cost
= $1.49 ≈ $0.0207 per oz ≈ 2.07¢ per oz
Number of ounces 72 oz
68-oz:
(This one is cheaper)
21. A fence is to be built around an outdoor basketball court measuring 40 ft × 30 ft. If fencing costs $4.75 per linear
foot, what will the fencing cost?
P = 2(L + W) = 2(40 ft + 30 ft) = 2(70 ft) = 140 ft
Cost = 140 × $4.75 = $665
22. A rollerskating rink is shown with dimensions in feet. How much will the hardwood flooring cost, based on a cost of
$6.50 per square foot?
40
Area of rectangle: A = LW = (70 ft)(40 ft) =
Area of circle: A = πr2 ≈ 3.14(20 ft)(20 ft) ≈
Total area
2,800
+1,256
4,056 × $6.50 = $26,364
70
23. You want to lay sod in an area measuring 74 ft × 62 ft. If sod costs 22¢ per square foot plus $35 for delivery, what is
the total cost?
A = LW = (74 ft)(62 ft) = 4,588 sq ft
Cost: (4,588 × $0.22) + $35 = $1,009.36 + $35 = $1,044.36
Chapter Review Problems
447
24. Refer to Problem 12. What is the cost to build the home, based on a cost per square foot of $120?
1,875 sq ft × $120 per sq ft = $225,000
25. Determine the total shipping weight of a carton containing two dozen cans of beans. Each can contains 12 oz of beans. Each
can (empty) weights 1 oz, and the cardboard carton (empty) weighs 10 oz. Express the total shipping weight in pounds.
Weight of each can, with beans: 12 oz + 1 oz
Number of cans
Total weight of cans, filled
Weight of carton
Total weight of carton, filled
13 oz
×24 oz
312 oz
+10 oz
322 oz = (322 ÷ 16) lb ≈ 20.13 pounds
26. You are adding a new family room to your home. The room measures 24 ft × 15 ft. Calculate the cost of carpeting
based on a cost of $21.50 per square yard. Assume there is no waste.
A = LW = (24 ft)(15 ft) = 360 sq ft = (360 ÷ 9) sq yd = 40 sq yd
Cost = 40 sq yd × $21.50 per sq yd = $860
27. A utility company is buying a right-of-way through a farm. If the strip of land is 2,640 ft long and 100 ft wide and the utility company is paying $22,000 per acre, how much will the farmer receive? Remember: Don’t round intermediate results.
A = LW = (2,640 ft)(100 ft) = 264,000 sq ft = (264,000 ÷ 43,560) acres ≈ 6.06060606 acres
6.06060606 acres × $22,000 per acre = $133,333.33
28. During a basketball game, you figure you ran an average of 65 ft each time you ran to the other end of the court. If you
changed ends a total of 150 times, how many miles (to the nearest hundredth of a mile) did you run during the game?
65 ft × 150 times = 9,750 ft = (9,750 ÷ 5,280) mi ≈ 1.85 mi
29. How many days will 100 yards of dental floss last if you use 15 inches each time you floss your teeth and you floss
each morning and evening?
100 yds = (100 × 36) in. = 3,600 in.
3,600 in. ÷ 30 in. per day = 120 days
Challenge problems
30. The distance from Miami to Seattle is 3,403 miles. A car is driven this distance using tires with a radius of 15 inches.
How many revolutions does each tire make?
C = 2πr ≈ 2(3.14)(15 in.) ≈ 94.20 in. (The car travels 94.20 inches for each revolution of the tires.)
3,403 mi = (3,403 × 5,280) ft = 17,967,840 ft = (17,967,840 × 12) in. = 215,614,080 in.
(The car travels 215,614,080 in.)
Tire revolutions: 215,614,080 in. ÷ 94.20 in. per revolution ≈ 2,288,897 revolutions
31. The earth has a circumference of about 25,000 miles. If a satellite is in orbit 200 miles above the surface of the earth,
how many miles does it travel each time it circles the earth?
Diameter of earth: d = c ≈ 25,000 mi ≈ 7,961.783439 mi
π
3.14
Diameter of satellite orbit: 7,961.783439 mi + 400 mi = 8,361.783439 mi
Circumference of orbit: C = πd ≈ 3.14(8,361.783439 mi) ≈ 26,256 mi
32. A bag of lawn fertilizer covers 550 square feet of lawn. Your lot measures 85 ft × 125 ft. In the middle is your home,
measuring 50 ft × 35 ft. Your driveway measures 25 ft × 30 ft. The remainder of your lot is covered with lawn. How
many bags of lawn fertilizer do you need?
Area lot: (85 ft)(125 ft)
Home: (50 ft)(35 ft)
Driveway: (25 ft)(30 ft)
Net area
10,625
- 1,750
- 750
8,125
sq ft
sq ft
sq ft
sq ft ÷ 550 sq ft per bag = 14.77 bags
Because you can’t buy part of a bag, you need 15 bags.
33. You have purchased some land for your dream home. The land is below street grade and requires fill dirt to bring it to
proper grade. Your land measures 115 ft × 280 ft and is an average of 27 in. below grade. How many cubic yards of
fill dirt are required?
27 ) ft = 2.25 ft
27 in. = ( 12
V = LWH = (115 ft)(280 ft)(2.25 ft) = 72,450 cu ft = (72,450
27 ) cu yd ≈ 2,683.33 cu yd
448
Chapter 22
Measurements: Real-World Applications
34. A farmer has land measuring 2,640 feet × 2,640 feet. The farmer is thinking about installing a circular sprinkling system to water crops, with the sprinkling system revolving around the center of the land. How many square feet of land
will not be farmed if a circular sprinkling system is installed?
2,640 ft
Total sq ft of land: A = LW = (2,640 ft)(2,640 ft) =
Sq ft in circular part: A = πr2 ≈ (3.14)(1,320 ft)(1,320 ft) =
Area not farmed
2,640 ft
6,969,600 sq ft
-5,471,136 sq ft
1,498,464 sq ft
35. Refer to Problem 34. What percent of the land will not be farmed?
Portion
(1,498,464 sq ft)
↑
6,969,600 sq ft
Base
Rate = Portion = 1,498,464 sq ft = 0.2150 = 21.50%
Base
Rate
(?)
6,969,600 sq ft
36. An 18-hole golf course has a total of 7,122 yards. If there are 125 yards from the clubhouse to the first tee, an average
of 50 yards between each green and the next tee, and 125 yards from the 18th green to the clubhouse, how many
miles would you walk for an 18-hole round (from clubhouse to clubhouse)? Hint to nongolfers: Each hole has a tee
(where the golfer begins the hole) and a green (where the hole is completed).
8,222 ) mi ≈ 4.67 mi
7,122 yd + 125 yd (to first hole) + (17 × 50 yd) + 125 yd (back to clubhouse) = 8,222 yd = ( 1,760
37. A certain alloy of steel weighs 475 pounds per cubic foot. What is the weight (in tons) of 500 steel bars if each measures 12 ft long and has a diameter of 43 of an inch?
Volume per bar (in cu in.): V = πr2h ≈ 3.14(.375 in)(.375 in.)(144 in.) ≈ 63.585 cu in.
Volume per bar (in cu ft): 63.585 cu in. = ( 63.585
1,728 ) cu ft ≈ 0.036796875 cu ft
Total volume of 500 bars: 0.036796875 cu ft × 500 = 18.3984375 cu ft
Weight of 500 bars: 18.3984375 cu ft × 475 lb per cu ft ≈ 8,739.257813 lb ≈ ( 8,739.257813
) T ≈ 4.37 T
2,000
38. You want to install a concrete driveway with dimensions of 27 ft 6 in. × 18 ft. The concrete is to be 4 in. thick. If concrete costs $85 per cubic yard, what is the total cost?
V = LWH = (27 ft 6 in.)(18 ft)(4 in.) ≈ (27.5 ft)(18 ft)( 13 ft) = 165 cu ft = (165
27 ) cu yd ≈ 6.111111111 cu yd
6.111111111 cu yd × $85 per cu yd = $519.44
39. A container made of wood measures 6 ft long, 4 ft deep, and 3 ft high. How many square feet of wood are required to
build the container? Remember, the container is closed on all sides.
Top and bottom: 2(6 ft × 4 ft)
Front and back: 2(6 ft × 3 ft)
Two ends: 2(4 ft × 3 ft)
Total
3 ft.
48
36
+24
108
sq ft
sq ft
sq ft
sq ft
4 ft.
6 ft.
40. Jilly Bean’s time for a 100-yard dash is 10.5 seconds. Calculate Jilly’s speed in miles per hour (mph) to the nearest
tenth.
100 yds = (100 ÷ 1,760) mi ≈ .05681818 mi
10.5 sec = (10.5 ÷ 60) min = .175 min = (.175 ÷ 60) hr ≈ .00291667 hr
miles per hour means miles ÷ number of hours, so: .05681818 mi ÷ .00291667 hr ≈ 19.5 mph
Chapter Review Problems
449
41. Refer to the newspaper article to the right. Assuming that the plot of land is a
rectangle, figure the length of the plot to the nearest hundredth of an inch.
A = LW
452 = L(24)
452 = L
24
18.83 ≈ L
Formula for area of rectangle
Substitute: W = 24 in.
Divide both sides by 24
Check answer: 18.83 in. × 24 in. ≈ 452 sq in.
Practice Test
For all problems, express the final answer with up to 2 decimal places. Assume π = 3.14.
1. A farmer wants to fence a field measuring 1,200 ft × 600 ft. How many feet of fencing are required?
P = 2(L + W) = 2(1,200 ft + 600 ft) = 2(1,800 ft) = 3,600 ft
2. A ball has a circumference of 31.5 inches. What is the diameter?
d = c ≈ 31.5 in. ≈ 10.03 in.
π
3.14
3. Find the area. Dimensions are in feet.
200
Rectangle: A = LW = (150 ft)(120 ft) =
Triangle: A = 12bh = 12(80 ft)(150 ft) =
Total area
150
18,000 sq ft
+ 6,000 sq ft
24,000 sq ft
120
4. A circular fountain is surrounded by a circular walkway 4 feet wide. The fountain has a diameter of 20 feet. What is the
area of the walkway?
Entire circle: A = πr2 ≈ 3.14(14 ft)(14 ft) ≈
Inner circle: A = πr2 ≈ 3.14(10 ft)(10 ft) ≈
Net area
10 ft
615.44 sq ft
- 314.00 sq ft
301.44 sq ft
4 ft
5. The city is excavating for a landfill. If the area measures 1,000 ft × 270 ft and must be dug to a depth of 12 ft, how many
cubic yards of earth must be removed?
) cu yd = 120,000 cu yd
V = LWH = (1,000 ft)(270 ft)(12 ft) = 3,240,000 cu ft = ( 3,240,000
27
6. Find the volume of a grain silo that has a diameter of 24 feet and a height of 45 feet.
V = πr2h ≈ 3.14(12 ft)(12 ft)(45 ft) ≈ 20,347.20 cu ft
7. You are thinking about building a home containing 2,320 sq ft. You have been told that homes cost about $95 to $120
per sq ft, depending on the quality, etc. Your builder gives you a cost of $242,000 for your home. Is that cost within the
$95 to $120 per sq ft range?
Cost per sq ft =
Cost
= $242,000 = $104.31 sq ft (Yes it is within range)
Number of sq ft 2,320 sq ft
8. You are thinking about buying some recreational land for a cabin, measuring 1,320 ft × 660 ft. How many acres is it?
A = LW = (1,320 ft)(660 ft) = 871,200 sq ft = ( 871,200
43,560 ) acres = 20 acres
450
Chapter 22
Measurements: Real-World Applications