Evaluate: Homework and Practice
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Determine which is denser.
1.
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2.
3.
Cylindrical logs of wood
Type of wood
Diameter (ft)
Height (ft)
Mass (lb)
Aspen
3.6
4.5
1,195
Juniper
3.0
6.0
1,487
Cylindrical bars of alloy
Alloy
Radius (cm)
Height (cm)
Mass (g)
Nichrome
3.9
27.2
10,800
Mild steel
4.6
18.8
9,840
Spherical tanks of liquefied gases
Liquefied Gas
Radius (m)
Mass (kg)
Oxygen (O 2), at -186°C
0.8
2477
1.2
514
Hydrogen (H 2), at -256°C
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Lesson 2
4.
Colorado has a population of 5,268,367. Its territory can be
modeled by a rectangle approximately 280 mi by 380 mi. Find
the approximate population density of Colorado.
5.
Tennessee has a population of 6,495,978. Its territory can be modeled by a trapezoid,
as shown in the figure. Each unit on the coordinate grid represents one mile. Find the
approximate population density of Tennessee.
200
y
D
C
x
0A
6.
200
B 400
New Hampshire has a population of 1,323,459. Its territory can be modeled by a
triangle, as shown in the figure. Each unit on the coordinate grid represents one mile.
Find the approximate population density of New Hampshire.
G
200
y
0
7.
E
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©EdgeofReason/Shutterstock
100
F x
100
A spherical gas tank has a 10 foot diameter. When filled with propane, it provides
358,000,000 BTUs. How many BTUs does 1 cubic foot of propane yield? Round to the
nearest thousand.
Module 4
220
Lesson 2
8.
9.
Ethan has collected information about the energy content of various fuels. Order
the fuels by their energy density from greatest to least. (​ 1 barrel = 42 gallons;
1 gallon = 8 pints)​
Fuel
Heat Content
Jet fuel
5,670,000 BTUs/barrel
Gasoline
160,937 BTUs/gallon
Home fuel
138,690 BTUs/gallon
Propane
11,417 BTUs/pint
A fuel tank has a volume of 32 gallons. When filled with biodiesel, it provides
4,000,000 BTUs. How many BTUs does 1 gallon of biodiesel yield?
10. A piece of marble has been machine-carved into the shape of a cone with the
dimensions shown. It has a mass of 169 kg. What is the density of the marble, to the
nearest kilogram per cubic meter?
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0.7 m
0.3 m
11. Metallurgy The purity of gold is measured in carats. 24-carat gold is pure gold, and has
a density of 19.3 g/c​m ​3​. 18-carat gold is often used for jewelry because it holds its shape
better than pure gold. An 18-carat gold ring, which is 75% pure gold, has a mass of 18 g.
What volume of pure gold was used to make the ring, to the nearest hundredth?
Module 4
221
Lesson 2
12. Agriculture The maximum grain yield for corn is achieved by planting at a
density of 38,000 plants per acre. A farmer wants to maximize the yield for the
field represented on the coordinate grid. Each unit on the coordinate grid
represents one foot. How many corn plants, to the nearest thousand, does the
farmer need? (​ Hint: 1 acre = 43,560 f​t ​2)​ ​
E
500
y
F
x
-500
0
500
G
H
-500
13. The density of water at 4°C is 1000 kg/​m ​3​. A cubic meter of water, when frozen to
–20°C, has a volume of 1.0065 m
​  ​3​. What is the density of ice at this temperature, to
the nearest tenth?
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Foote/age fotostock
14. Space A launch vehicle is designed to carry up to 35 tons of payload into orbit.
When fully fueled, it will contain 1,216,000 kg of liquid oxygen (L​O 2​ ​) at a density of
1155 kg/​m ​3​and 102,000 kg of liquid hydrogen (L​H 2​ ​) at a density of 71 kg/​m ​3​. What is
the total volume of liquefied gases carried by the launch vehicle, to the nearest tenth?
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Lesson 2
15. Manila, Philippines, has one of the highest population densities in the world with
111,002 people/m​i ​2​. Manila’s total population is 1,652,171. How large is Manilla, to
the nearest tenth of a square mile?
16. Multistep A building has apartments on 67 floors and each floor measures 110 feet
by 85 feet. Currently, 2340 people live in the building. Find the population density of
the building to the nearest person per square mile, in terms of the area occupied by
the building at street level. Also find the population density of the building in terms
of its total floor area. (Hint: 1 m
​ i ​2​= 27,878,400 f​ t ​2​)
17. The caloric density of foods is a useful tool when comparing calorie counts. The table
shows typical serving sizes for several foods and the number of calories per serving.
Complete the fourth column. Then use the final column to number the foods from
the lowest caloric density to the highest. Round to the nearest calorie per gram.
Cal per
Grams (g) Calories
100 g
(Cal)
1 cubic inch cheddar cheese
17
69
1 large hard boiled egg
50
78
1 medium apple
138
72
1.5 ounces raisins
43
129
H.O.T. Focus on Higher Order Thinking
18. Analyze Relationships The graph shows the relationship
between mass and volume for pure silver. Use the graph to
determine the density of pure silver to the nearest tenth and
explain your method.
100
Mass of silver (g)
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Food
y
50
x
0
5
10
Volume of silver (cm3)
Module 4
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Lesson 2