3.5 Chapter Review

Izabela Mazur

CHAPTER 3 Measurement, Perimeter, Area, and Volume

3.5 Chapter Review

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.	72.
73.	74.
75.	76.

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

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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.

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.
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.

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

Review Exercises