Deck 9: The Nature of Networks and Graph Theory

Question 1

Find the volume of the solid correct to the nearest unit. ​a​ = 4, ​b​ = 7, ​h​ = 9.
​ ​

A) 99 cm ³
B) 252 cm ³
C) 84 cm ³
D) 28 cm ³
E) 126 cm ³

Answer 1

84 cm ³

Question 2

11 L is the measure of __________ (capacity, distance, weight, temperature).

Answer 2

capacity

Question 3

Water boils at __________ °C.

Answer 3

100

Question 4

Make the indicated conversions. ​
1 mm
​

A) 1,000 mL
B) 0.1 mi
C) 0.1 cm
D) 0.001 km
E) 1,000 mg

Question 5

Find the surface area of the solid correct to the nearest square unit. (Note that the container does not have top.) ​
​​r​ = 2.8​, ​h​ = 4.4.
​ ​

A) 77 cm ²
B) 12 cm ²
C) 204 cm ²
D) 102 cm ²
E) 108 cm ²

Question 6

Name the metric unit you would use to measure the quantity below: ​
The distance from New York to Chicago.
​

A) kilogram
B) pounds
C) kilometer
D) liter
E) Celsius

Question 7

Find the surface area of the solid correct to the nearest square unit. (Note that the container does not have top.)
​r​ = 1.4​, ​h​ = 5.7.
​ ​
__________ cm²

Question 8

Water boils at what temperature? ​

A) 100 ^o C
B) 200 ^o C
C) 805 ^o C
D) 78 ^o C
E) 123 ^o C

Question 9

Find the volume of the solid correct to the nearest unit.
​​a​ = 5, ​b​ = 6, ​h​ = 6.
​ ​
__________ cm³

Question 10

Find the volume and the surface area of the solid correct to the nearest unit.​ r = 4, h = 9.
​ ​

A) 124 in ² and 151 in ³
B) 25 in ² and 324 in ³
C) 50 in ² and 64 in ³
D) 254 in ² and 729 in ³
E) 151 in ² and 124 in ³

Question 11

Name the metric unit you would use to measure the mass of an automobile.

Question 12

Find the volume of the solid correct to the nearest unit.​
​a​ = 12​, ​b​ = 5, ​c​ = 13, ​h​ = 4.
​ ​
__________ in³

Question 13

If the radius of a sphere is multiplied by two, what effect does that have on the surface area?
​
The effect is __________-fold __________ (increase, decrease).

Question 14

10 kg is a measure of what? ​

A) length
B) mass
C) temperature
D) distance
E) capacity

Question 15

Make the indicated conversions.
​
1 m = __________ km.

Question 16

Suppose it takes 11 hours to fill a rectangular swimming pool of uniform depth. How long will it take to fill a similarly shaped swimming pool if all of the dimensions are doubled? ​

A) 88 hr.
B) 22 hr.
C) 11 hr.
D) 44 hr.
E) 176 hr.

Question 17

Suppose it takes 12 hours to fill a rectangular swimming pool of uniform depth. How long will it take to fill a similarly shaped swimming pool if all of the dimensions are doubled?
​
__________ hours

Question 18

Find the volume and the surface area of the solid correct to the nearest unit.​
​r​ = 4​, ​h​ = 8.
​ ​
The volume is __________ in³.
​
The surface area is __________ in².

Question 19

Find the volume of the solid correct to the nearest unit. ​
​a​ = 4​, b​ = 15, ​c​ = 15.524175, ​h​ = 6.
​ ​

A) 180 in ³
B) 360 in ³
C) 60 in ³
D) 233 in ³
E) 62 in ³

Question 20

If the radius of a sphere is multiplied by 3, what effect does that have on the area? ​

A) 27 - fold increase
B) 1.5 - fold decrease
C) 9 - fold increase
D) 3 - fold increase
E) doesn't change

Question 21

How much coffee does an average cup contain?
​
Without measuring, pick the best answer.
​
__________ (750, 250, 900) ml.

Question 22

Find the capacity of the container, when ​a​ = 20, ​b​ = 15, ​c​ = 30. ​ ​

A) 15 L
B) 10 L
C) 12 L
D) 13 L
E) 9 L

Question 23

Find the outside surface area, when ​a = ​2, b = 6, c = 2. ​
​ ​

A) 60 m ²
B) 44 m ²
C) 48 m ²
D) 56 m ²
E) 12 m ²

Question 24

Consider the plot plan shown in the figure below. How many cubic yards of sawdust are needed for preparation of the lawn area if it is to be spread to a depth of 2 inches?
​
Give your answer to the nearest cubic yard.
​ ​
__________ yd³

Question 25

Find the volume of the solid below, when ​a​ = 10, ​b​ = 20, ​​c​ = 2. ​ ​

A) 500 mm ³
B) 400 mm ³
C) 471 mm ³
D) 8 mm ³
E) 444 mm ³

Question 26

Consider the plot plan shown in the figure below. How many cubic yards of sawdust are needed for preparation of the lawn area if it is to be spread to a depth of 5 inches? ​
Give your answer to the nearest cubic yard.
​ ​

A) 11 yd ³
B) 8 yd ³
C) 2 yd ³
D) 9 yd ³
E) 6 yd ³

Question 27

Find the volume of the refrigerator, when ​a​ = 34, ​b​ = 30, ​c​ = 60. Round your answer to the nearest hundredth.
​ ​
__________ ft³

Question 28

The prefix milli- means __________.

A) one-hundredth
B) one thousand
C) one million
D) one-thousandth
E) one-millionth

Question 29

The prefix centi- means __________ (one thousand, one-thousandth, one-hundredth).

Question 30

Find the volume of the refrigerator, when ​a​ = 37, ​b​ = 34, ​c​ = 68. Round your answer to the nearest thousandth. ​
​ ​

A) 55.005 ft ³
B) 58.241 ft ³
C) 7,128.667 ft ³
D) 39.604 ft ³
E) 49.505 ft ³

Question 31

Find the volume of each by counting the number of cubic centimeters in each box. ​ ​

A) 23 cm³
B) 6 cm³
C) 12 cm³
D) 16 cm³
E) 18 cm³

Question 32

Find the outside surface area, when ​a​ = 6, h​ = 7. ​
​ ​

A) 84 in. ²
B) 204 in. ²
C) 168 in. ²
D) 120 in. ²
E) 78 in. ²

Question 33

How much coffee does an average cup contain? ​
Without measuring, pick the best answer.
​

A) 250 ml
B) 750 ml
C) 1 L
D) 500ml
E) 2 L

Question 34

Find the outside surface area, when ​a​ = 1, ​b​ = 4, ​c​ = 1.
​ ​
__________ m²

Question 35

Find the volume of the solid below, when ​a​ = 5, ​b​ = 20, ​c​ = 1.
​ ​
__________ mm³

Question 36

Pick the best choice by estimating. Do not measure. For metric measurements, do not attempt to convert to the U.S. system. ​The area of a dollar bill is __________.
​

A) 6 in.²
B) 18 in.
C) 18 in.²
D) 0.06 in.²
E) 3 in.²

Question 37

Find the outside surface area, when ​a​ = 4, ​h​ = 6.
​ ​
__________ in²

Question 38

Find the capacity of the container, when ​a​ = 20, ​b​ = 25, ​c​ = 30. Give your answer to one decimal place, if required.
​ ​
__________ L

Question 39

Pick the best choice by estimating. Do not measure. For metric measurements, do not attempt to convert to the U.S. system. The area of a classroom is __________.
​

A) 0.5 acre
B) 1,000 ft²
C) 0.15 acre
D) 100 ft²
E) 0.55 acre

Question 40

Find the volume of each solid by counting the number of cubic centimeters in each box.
​ ​
__________ cm³

Question 41

If the lengths of three sides of a triangle are known, then the following formula, known as Hero's (or Heron's) formula is sometimes used:
​ ​​where a, b, and c are the given lengths of the sides, and . Use this formula to find the area of a triangle with the lengths given below (correct to the nearest square foot).
​ , , and ​
__________ ft²

Question 42

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.)
​ ​ ​
__________ in.²

Question 43

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.) Use ​ ​

A) 900.0 in.²
B) 706.9 in.²
C) 176.7 in.²
D) 225.0 in.²
E) 353.4 in.²

Question 44

Find the area of the shaded region. ​ , ​

A) 3,741 ft²
B) 130 ft²
C) 3,749 ft²
D) 3,725 ft²
E) 260 ft²

Question 45

Find the circumference if . Round approximate answer to two decimal places. ​ ​

A) 7.54 m
B) 15.08 m
C) 12.06 m
D) 17.74 m
E) 18.10 m

Question 46

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.) ​ , ​

A) ​16 ft²
B) ​4 ft²
C) 10​ ft²
D) ​8 ft²
E) ​20 ft²

Question 47

If the lengths of three sides of a triangle are known, then the following formula, known as Hero's (or Heron's) formula is sometimes used: ​ ​where a, b, and c are the given lengths of the sides, and . Use this formula to find the area of a triangle with the lengths given below (correct to the nearest square foot).
​ ft, ft, and ft
​

A) 41 ft²
B) 3 ft²
C) 6 ft²
D) 13 ft²
E) 14 ft²

Question 48

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.) ​ ​

A) 7.1 dm²
B) 9 dm²
C) 2.25 dm²
D) 2.3 dm²
E) 28.3 dm²

Question 49

If a certain type of fabric comes in a bolt 4 feet wide, how long a piece must be purchased to have 32 square feet?
​
__________ feet

Question 50

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.) ​ ​
__________ dm²

Question 51

Find the area of the shaded region. ​ , ​

A) 54 in.²
B) 12 in.²
C) 13.5 in.²
D) 27 in.²
E) 24 in.²

Question 52

If a certain type of fabric comes in a bolt 4 feet wide, how long a piece must be purchased to have 48 square feet? ​

A) 12 ft
B) 20 ft
C) 44 ft
D) 8 ft
E) 576 ft

Question 53

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit, if required.)
​ , ​
__________ ft²

Question 54

Find the perimeter by using the appropriate formula, if and . ​ ​

A) 18 ft
B) 30 ft
C) 9 ft
D) 15 ft
E) 36 ft

Question 55

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit, if required.)
​ , ​
__________ ft².

Question 56

Pick the best choice by estimating. Do not measure. For metric measurements, do not attempt to convert to the U.S. system. The hardest part of the transition to the metric system is the transition to thinking in metrics. ​
The perimeter of a dollar bill is about __________.
​

A) 36 in.
B) 46 in.
C) 6 in.
D) 18 in.
E) 56 in.

Question 57

Pick the best choice by estimating. Do not measure. For metric measurements, do not attempt to convert to the U.S. system.
​
The area of the floor space of the Superdome in New Orleans is __________.

Question 58

Pick the best choice by estimating. Do not measure. For metric measurements, do not attempt to convert to the U.S. system.
​
The area of the front cover of this textbook is __________.

Question 59

The prefix milli- means __________. ​

A) one-millionth
B) one thousand
C) one-hundredth
D) one-thousandth
E) one-hundred

Question 60

Find the area of the shaded region. (Assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit, if required.) ​, ​ ​
__________ in.²

Question 61

Find the perimeter by using the appropriate formula, if and .
​ ​
__________ ft

Question 62

Pick the best choice by estimating. Do not measure. For metric measurements, do not attempt to convert to the U.S. system. The hardest part of the transition to the metric system is the transition to thinking in metrics.
The perimeter of a dollar bill is about __________ (6, 46, 18) in.

Question 63

The prefix centi- means __________ (one-hundredth, one thousand, one-thousandth).

Question 64

Find the distance around the figure below by using the appropriate formula. Round your answer to two decimal places.
​ ​
Where ​
__________cm

Question 65

Find the distance around the figure below by using the appropriate formula. Round your answer to two decimal places.
​ ​
Where ​
__________in.

Question 66

The perimeter is 45 in. Find the lengths of the sides.
​ ​ ​ ​

Question 67

Suppose that we fit a band tightly around the earth at the equator. We wish to raise the band so that it is uniformly supported 10 ft above the earth at the equator. How much extra length would have to be added to the band (not the supports) to do this. Please, round your answer to the nearest ft.
​ ​
__________ ft

Question 68

Find the circumference, if . Round approximate answer to two decimal places.
​ ​
__________m

Question 69

The perimeter of this pentagon is 280 cm. Find the lengths of the sides. ​ ​

A)
B)
C)
D)
E)

Question 70

Find the distance around the figure below by using the appropriate formula, if , , , , . Round approximate answers to two decimal places. ​ ​

A) 15.20 cm
B) 10.74 cm
C) 21.48 cm
D) 14.60 cm
E) 27.77 cm

Question 71

Suppose that we fit a band tightly around the earth at the equator. We wish to raise the band so that it is uniformly supported 7 ft above the earth at the equator. How much extra length would have to be added to the band (not the supports) to do this. ​ ​

A) about 37 ft
B) about 44 ft
C) about 49 ft
D) about 35 ft
E) about 88 ft

Question 72

Find the distance around the figure below by using the appropriate formula, if . Round approximate answers to two decimal places. ​ ​

A) 35.71 in.
B) 51.42 in.
C) 41.42 in.
D) 25.71 in.
E) 71.42 in.

Question 73

Find the distance around the figure below by using the appropriate formula, if , . Round approximate answer to two decimal places. ​ ​

A) 16.28 cm
B) 9.14 cm
C) 11.14 cm
D) 14.28 cm
E) 20.57 cm

Question 74

The perimeter of is 108 in. Find the lengths of the sides. ​ ​

A) 24 in., 36 in., 96 in.
B) 24 in., 36 in., 48 in.
C) 26 in., 39 in., 48 in.
D) 24 in., 36 in., 60 in.
E) 26 in., 39 in., 52 in.

Question 75

The perimeter of this pentagon is 280 in. Find the lengths of the sides.
​ ​ ​ ​ ​ ​

Question 76

Find the distance around the figure below by using the appropriate formula.
​ ​
Where ​
__________cm