CHAPTER 3 Measurement, Perimeter, Area, and Volume

3.5 Chapter Review

Review Exercises

Systems of Measurement

In the following exercises, convert between Imperial units. Round to the nearest tenth.

1. A picture frame is 42 inches wide. Convert the width to feet. 2. A floral arbor is 7 feet tall. Convert the height to inches.
3. A playground is 45 feet wide. Convert the width to yards. 4. Kelly is 5 feet 4 inches tall. Convert her height to inches.
5. An orca whale in the Salish Sea weighs 4.5 tons. Convert the weight to pounds. 6. The height of Mount Shasta is 14,179 feet. Convert the height to miles.
7. How many tablespoons are in a quart? 8. The play lasted 1\frac{3}{4} hours. Convert the time to minutes.
9. Trinh needs 30 cups of paint for her class art project. Convert the volume to gallons. 10. Naomi’s baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.

In the following exercises, solve, and state your answer in mixed units.

11. Every day last week, Pedro recorded the amount of time he spent reading. He read for 50,25,83,45,32,60,\text{and}\phantom{\rule{0.2em}{0ex}}135 minutes. How much time, in hours and minutes, did Pedro spend reading? 12. John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?
13. Dalila wants to make pillow covers. Each cover takes 30 inches of fabric. How many yards and inches of fabric does she need for 4 pillow covers? 14. Fouad is 6 feet 2 inches tall. If he stands on a rung of a ladder 8 feet 10 inches high, how high off the ground is the top of Fouad’s head?

In the following exercises, convert between metric units.

15. Mount Everest is 8,850 metres tall. Convert the height to kilometres. 16. Donna is 1.7 metres tall. Convert her height to centimetres.
17. One cup of yogurt contains 13 grams of protein. Convert this to milligrams. 18. One cup of yogurt contains 488 milligrams of calcium. Convert this to grams.
19. A bottle of water contained 650 millilitre s. Convert this to litres. 20. Sergio weighed 2.9 kilograms at birth. Convert this to grams.

In the following exercises, solve.

21. Selma had a \text{1-liter} bottle of water. If she drank 145 millilitres, how much water, in millilitres, was left in the bottle? 22. Minh is 2 metres tall. His daughter is 88 centimetres tall. How much taller, in metres, is Minh than his daughter?
23. One ounce of tofu provides 2 grams of protein. How many milligrams of protein are provided by 5 ounces of tofu? 24. One serving of cranberry juice contains 30 grams of sugar. How many kilograms of sugar are in 30 servings of cranberry juice?

In the following exercises, convert between Imperial and metric units. Round to the nearest tenth.

25. A college basketball court is 84 feet long. Convert this length to metres. 26. Majid is 69 inches tall. Convert his height to centimetres.
27. Lucas weighs 78 kilograms. Convert his weight to pounds. 28. Caroline walked 2.5 kilometres. Convert this length to miles.
29. A box of books weighs 25 pounds. Convert this weight to kilograms. 30. Steve’s car holds 55 litres of gas. Convert this to gallons.

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

31. 23°F 32. 95°F
33. 64°F 34. 20°F

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

35. -5°C 36. 30°C
37. 24°C 38. -12°C

Understand Linear, Square, Cubic Measure

In the following exercises, would you measure each item using linear, square, or cubic measure?

39. amount of sand in a sandbag 40. height of a tree
41. size of a patio 42. length of a highway

In the following exercises, find a) the perimeter b) the area of each figure

43. Three squares are shown, in a sideways L shape. 44. Five squares are shown, in a T-shape. There are three squares across the top and three squares down.

Use Properties of Rectangles

In the following exercises, find the a) perimeter b) area of each rectangle

45. The length of a rectangle is 42 metres and the width is 28 metres. 46. The length of a rectangle is 36 feet and the width is 19 feet.
47. A sidewalk in front of Kathy’s house is in the shape of a rectangle 4 feet wide by 45 feet long. 48. A rectangular room is 16 feet wide by 12 feet long.

In the following exercises, solve.

49. Find the length of a rectangle with perimeter of 220 centimetres and width of 85 centimetres. 50. Find the width of a rectangle with perimeter 39 and length 11.
51. The area of a rectangle is 2356 square metres. The length is 38 metres. What is the width? 52. The width of a rectangle is 45 centimetres. The area is 2700 square centimetres. What is the length?
53. The length of a rectangle is 12 centimetres more than the width. The perimeter is 74 centimetres. Find the length and the width. 54. The width of a rectangle is 3 more than twice the length. The perimeter is 96 inches. Find the length and the width.

Use Properties of Triangles

In the following exercises, solve using the properties of triangles.

55. Find the area of a triangle with base 18 inches and height 15 inches. 56. Find the area of a triangle with base 33 centimetres and height 21 centimetres.
57. A triangular road sign has base 30 inches and height 40 inches. What is its area? 58. If a triangular courtyard has sides 9 feet and 12 feet and the perimeter is 32 feet, how long is the third side?
59. A tile in the shape of an isosceles triangle has a base of 6 inches. If the perimeter is 20 inches, find the length of each of the other sides. 60. Find the length of each side of an equilateral triangle with perimeter of 81 yards.
61. The perimeter of a triangle is 59 feet. One side of the triangle is 3 feet longer than the shortest side. The third side is 5 feet longer than the shortest side. Find the length of each side. 62. One side of a triangle is three times the smallest side. The third side is 9 feet more than the shortest side. The perimeter is 39 feet. Find the lengths of all three sides.

Use Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

63. The height of a trapezoid is 8 feet and the bases are 11 and 14 feet. What is the area? 64. The height of a trapezoid is 5 yards and the bases are 7 and 10 yards. What is the area?
65. Find the area of the trapezoid with height 25 metres and bases 32.5 and 21.5 metres. 66. A flag is shaped like a trapezoid with height 62 centimetres and the bases are 91.5 and 78.1 centimetres. What is the area of the flag?

Use Properties of Circles

In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.

67. A circular mosaic has radius 3 metres. Find the

a) circumference

b) area of the mosaic

68. A circular fountain has radius 8 feet. Find the

a) circumference

b) area of the fountain
69. Find the diametre of a circle with circumference 150.72 inches. 70. Find the radius of a circle with circumference 345.4 centimetres

Find the Area of Irregular Figures

In the following exercises, find the area of each shaded region.

71. A geometric shape is shown, formed by two rectangles. The top is labeled 8. The width of the top rectangle is labeled 3. The right side of the figure is labeled 5. The width of the bottom rectangle is labeled 3. 72. A geometric shape is shown. It is a U-shape. The base is labeled 5, the height 6. The horizontal and vertical lines at the top are labeled 2.
73. A geometric shape is shown. It is formed by two triangles. The shared base of the two triangles is labeled 20. The height of each triangle is labeled 15. 74. A geometric shape is shown. It is a trapezoid with a triangle attached to the top on the right side. The height of the trapezoid is labeled 8, the bottom base is labeled 12, and the top is labeled 9. The height of the triangle is labeled 8.
75. A geometric shape is shown. It is a rectangle with a semi-circle attached to the top. The base of the rectangle, also the diametre of the semi-circle, is labeled 10. The height of the rectangle is labeled 16. 76. A geometric shape is shown. It is a triangle with a semicircle attached. The base of the triangle, also the diametre of the semi-circle, is labeled 5. The height of the triangle is also labeled 5.

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find the a) volume b) surface area of the rectangular solid

77. A rectangular solid with length 14 centimetres, width 4.5 centimetres, and height 10 centimetres 78. A cube with sides that are 3 feet long
79. A cube of tofu with sides 2.5 inches 80. A rectangular carton with length 32 inches, width 18 inches, and height 10 inches

Find Volume and Surface Area of Spheres

In the following exercises, find the a) volume b) surface area of the sphere.

81. a sphere with radius 4 yards 82. a sphere with radius 12 metres
83. a baseball with radius 1.45 inches 84. a soccer ball with radius 22 centimetres

Find Volume and Surface Area of Cylinders

In the following exercises, find the a) volume b) surface area of the cylinder

85. A cylinder with radius 2 yards and height 6 yards 86. A cylinder with diametre 18 inches and height 40 inches
87. A juice can with diametre 8 centimetres and height 15 centimetres 88. A cylindrical pylon with diametre 0.8 feet and height 2.5 feet

Find Volume of Cones

In the following exercises, find the volume of the cone.

89. A cone with height 5 metres and radius 1 metre 90. A cone with height 24 feet and radius 8 feet
91. A cone-shaped water cup with diametre 2.6 inches and height 2.6 inches 92. A cone-shaped pile of gravel with diametre 6 yards and height 5 yards

Review Answers

1. 3.5 feet 3. 15 yards 5. 9000 pounds
7. 64 tablespoons 9. 1.9 gallons 11. 7 hours 10 minutes
13. 3 yards, 12 inches 15. 8.85 kilometres 17. 13,000 milligrams
19. 0.65 litres 21. 855 millilitre s 23. 10,000 milligrams
25. 25.6 metres 27. 171.6 pounds 29. 11.4 kilograms
31. -5°C 33. 17.8°C 35. 23°F
37. 75.2°F 39. cubic 41. square
43.

a) 8 units

b) 3 sq. units

 45.

a) 140 m

b) 1176 sq. m

 47.

a) 98 ft.

b) 180 sq. ft.
49. 25 cm 51. 62 m 53. 24.5 in., 12.5 in.
55. 135 sq. in. 57. 600 sq. in. 59. 7 in., 7 in.
61. 17 ft., 20 ft., 22 ft. 63. 100 sq. ft. 65. 675 sq. m
67.

a) 18.84 m

b) 28.26 sq. m

 69. 48 in. 71. 30 sq. units
73. 300 sq. units 75. 199.25 sq. units 77.

a) 630 cu. cm

b) 496 sq. cm
79.

a) 15.625 cu. in.

b) 37.5 sq. in.

 81.

a) 267.95 cu. yd.

b) 200.96 sq. yd.

 83.

a) 12.76 cu. in.

b) 26.41 sq. in.
85.

a) 75.36 cu. yd.

b) 100.48 sq. yd.

 87.

a) 753.6 cu. cm

b) 477.28 sq. cm

 89. 5.233 cu. m
91. 4.599 cu. in.

Practice Test

In the following exercises, solve using the appropriate unit conversions.

1. One cup of milk contains 276 milligrams of calcium. Convert this to grams. \text{(1 milligram}=\text{0.001 gram)} 2. Azize walked 4\frac{1}{2} miles. Convert this distance to feet. \text{(1 mile}=\text{5,280 feet).}
3. Janice ran 15 kilometres. Convert this distance to miles. Round to the nearest hundredth of a mile. \text{(1 mile}=\text{1.61 kilometres)} 4. Larry had 5 phone customer phone calls yesterday. The calls lasted 28,44,9,75,\text{and}\phantom{\rule{0.2em}{0ex}}55 minutes. How much time, in hours and minutes, did Larry spend on the phone? \text{(1 hour}=\text{60 minutes)}
5. Use the formula F=\frac{9}{5}C+32 to convert 35°C to degrees \text{F} 6. Yolie is 63 inches tall. Convert her height to centimetres. Round to the nearest centimetre. \text{(1 inch}=\text{2.54 centimetres)}
7. A triangular poster has base 80 centimetres and height 55 centimetres. Find the area of the poster. 8. The length of a rectangle is 2 feet more than five times the width. The perimeter is 40 feet. Find the dimensions of the rectangle.
9. A circular pool has diametre 90 inches. What is its circumference? Round to the nearest tenth. 10. A trapezoid has height 14 inches and bases 20 inches and 23 inches. Find the area of the trapezoid.
11. Find the volume of a rectangular room with width 12 feet, length 15 feet, and height 8 feet.

12. Find the area of the shaded region. Round to the nearest tenth.

A geometric shape is shown. It is a rectangle with a semi-circle attached on the left and a triangle attached on the right. The height of the rectangle, also the height of the triangle and the diametre of the semi-circle, is labeled 4. The base of the figure is labeled 10. The top of the rectangle is labeled 7.
13. A traffic cone has height 75 centimetres. The radius of the base is 20 centimetres. Find the volume of the cone. Round to the nearest tenth. 14. A coffee can is shaped like a cylinder with height 7 inches and radius 5 inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.

Practice Test Answers

1. .276 grams 2. 23760 feet 3. 9.317 miles
4. 211 minutes, 3 hours and 31 minutes 5. 95°F 6. 160 centimetres
7. 2,200 square centimetres 8. 11 feet, 9 feet 9. 282.6 inches
10. 201 feet 11. 1,440 cubic feet 12. 10.3 square inches
13. 31,400 cubic inches 14. a)  534.1 square inches b) 1335 cubic inches

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Introductory Algebra Copyright © 2021 by Izabela Mazur is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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