Name: __________________________________ Date: __________ Period: ___
Propensity for Density - Activity 2
Part I
1. A loaf of bread has a volume of 2000 cm3 and a mass of 450 g. What is the density of the
bread?
2. A piece of wood has a density of 0.6 g/cm3 and a volume of 1.5 cm3. What is the mass of the
piece of wood?
3. A small rock has a density of 1.4 g/cm3 and a mass of 62 grams. What is its volume?
4. A spherical balloon can hold 1.2 liters of helium. The balloon has a mass of 26 milligrams
when empty. Helium has a density of 0.1785 grams per liter. What is the mass of the
balloon when it is filled with helium?
5. Assume a U.S. coin is cylindrical, with
use the following specifications from the
U.S. Mint for coins presently in production for 2014 United States Mint Annual Sets
(http://www.usmint.gov/about_the_mint/index.cfm?action=Coin_specifications) to calculate
the volume and density of each type of coin.
Denomination Cent (Penny)
Nickel
Dime
Quarter Dollar
2.500 g
5.000 g
2.268 g
5.670 g
Diameter
19.05 mm
21.21 mm
17.91 mm
24.26 mm
Thickness
1.52 mm
1.95 mm
1.35 mm
1.75 mm
Weight (mass)
Volume
Density
a. Which of the U.S. coins listed has the highest density? __________________________
b. Which of the U.S. coins listed has the lowest density? ___________________________
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Part II
6. Use the following information from the 2012 projections for each state from the U.S. Census
Bureau (https://www.census.gov/population/projections/data/national/2012.html) to calculate
the population density of each state in both people per square kilometer and people per
square mile.
State
Alaska
Population
Land Area
(Sq. Kms)
Land Area
(Sq. Miles)
686,293 1,481,346.00
571,951
18,328,340
139,760.29
53,927
Idaho
1,523,816
214,313.75
82,747
Massachusetts
6,497,967
20,305.51
7,840
967,440
376,977.95
145,552
New Jersey
8,682,661
19,209.94
7,417
New York
19,490,297
122,283.70
47,214
1,050,788
2,706.54
1,045
24,326,974
678,051.12
261,797
Florida
Montana
Rhode Island
Texas
Pop. Density Pop. Density
(Sq. Km)
(Sq. Mile)
a. Which of the U.S. states listed has the highest population density? _____________
b. Which of the U.S. states listed has the lowest population density? ______________
Part III
7. Fifty students exercised in the school gymnasium, each produced about 320 BTUs (British
Thermal Units) of heat. The gymnasium is 100 feet long, 80 feet wide, and 20 feet high.
How many BTUs per cubic foot did the students produce?
8. Approximately 175 chopped walnut pieces were stirred into a brownie mix that fills a 9”
diameter pan that is 1” deep. What is the density of the walnut pieces? How many walnut
pieces would you expect in a 2”  2”  1” brownie serving?
9. The clerk at the local pet store said, “Perfect aquarium density is when there are 1.5 gallons
of water for every 1 inch of fish.” An aquarium magazine has a photograph of a beautiful
aquarium with perfect density that contains 10 fish, each 3 inches long. What is the density
of the aquarium? How many gallons of water are in the aquarium in the photograph?
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Part IV
10. You want to open a dog walking business, and are considering the east side of town and the
west side of town. You will open the business wherever the density of dogs per home is
greater than 0.35. According to town records, the dog population of the 20-city block east
side is 6 dogs per block with 18 homes per block. The dog population of the 30-city block
west side is 4 dogs per block with 10 homes per block. Where, if anywhere, should you open
your new dog walking business?
Number of
Dogs per Block
Number of
Homes per Block
Number of
Dogs per Home
East Side of Town
West Side of Town
A. east side of town only
C. both east side and west side of town
B. west side of town only
D. neither east side nor west side of town
11. While in the school library you notice some book sections seem to be more “crowded” with
regard to shelf space. Use the data provided by the librarian to determine the density of each
section of the school library.
Fiction
Non-Fiction
Reference
Number of
books
372
528
257
Total shelf space
in square feet
400
656
395
Density
(books/ft2)
Suppose you have a piece of cotton fabric that measures
36”  44” and has a total of 142,560 threads.
a. Determine the thread count (TPI) of the piece of cotton fabric.
30 threads
← 1 inch →
12. Thread count or TPI (threads per inch) is a measure of the coarseness or fineness of fabric. It
is the total number of vertical and horizontal threads in one square inch. It is measured by
counting the number of threads along two sides (across and up) of the square inch, added
together. It is usually used in regard to cotton linens such as bed sheets. Suppose you have a
bed sheet with a thread count of 60, this could mean there are 30 horizontal threads and 30
vertical threads per square inch as shown in the diagram.
← 1 inch →
30 threads
b. Estimate the number of threads on each of the two sides of one inch of the cotton fabric.
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Key
Name: __________________________________
Date: __________ Period: ___
Propensity for Density - Activity 2
Part I
1. A loaf of bread has a volume of 2000 cm3 and a mass of 450 g. What is the density of the
bread?
= 0.225 g/cm3
2. A piece of wood has a density of 0.6 g/cm3 and a volume of 1.5 cm3. What is the mass of the
piece of wood?
rams
3. A small rock has a density of 1.4 g/cm3 and a mass of 62 grams. What is its volume?
cm3, with attention to significant digits it is 44 cm3
4. A spherical balloon can hold 1.2 liters of helium. The balloon has a mass of 26 milligrams
when empty. Helium has a density of 0.1785 grams per liter. What is the mass of the
balloon when it is filled with helium?
rams 0.2142 + 0.026 = 0.2402 grams
5. Assume a U.S. coin is cylindrical, with
use the following specifications from the
U.S. Mint for coins presently in production for 2014 United States Mint Annual Sets
(http://www.usmint.gov/about_the_mint/index.cfm?action=Coin_specifications) to calculate
the volume and density of each type of coin.
Denomination Cent (Penny)
Nickel
Dime
Quarter Dollar
2.500 g
5.000 g
2.268 g
5.670 g
Diameter
19.05 mm
21.21 mm
17.91 mm
24.26 mm
Thickness
1.52 mm
1.95 mm
1.35 mm
1.75 mm
433.23 mm3
688.97 mm3
340.10 mm3
808.92 mm3
0.005 g/mm3
0.007 g/mm3
0.006 g/mm3
0.007 g/mm3
Weight (mass)
Volume =
r2 h
Density = m/v
Nickel and Quarter
a. Which of the U.S. coins listed has the highest density? __________________________
Penny
b. Which of the U.S. coins listed has the lowest density? ___________________________
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Part II
6. Use the following information from the 2012 projections for each state from the U.S. Census
Bureau (https://www.census.gov/population/projections/data/national/2012.html) to calculate
the population density of each state in both people per square kilometer and people per
square mile.
State
Alaska
Land Area
(Sq. Kms)
Population
Land Area
(Sq. Miles)
686,293 1,481,346.00
Pop. Density Pop. Density
(Sq. Km)
(Sq. Mile)
571,951
0.46
1.19
18,328,340
139,760.29
53,927
131.14
339.87
Idaho
1,523,816
214,313.75
82,747
7.11
18.41
Massachusetts
6,497,967
20,305.51
7,840
320.01
828.82
967,440
376,977.95
145,552
2.56
6.64
New Jersey
8,682,661
19,209.94
7,417
451.98
1,170.64
New York
19,490,297
122,283.70
47,214
159.38
412.80
1,050,788
2,706.54
1,045
388.24
1,005.53
24,326,974
678,051.12
261,797
35.87
92.92
Florida
Montana
Rhode Island
Texas
New Jersey
a. Which of the U.S. states listed has the highest population density? _____________
Alaska
b. Which of the U.S. states listed has the lowest population density? ______________
Part III
7. Fifty students exercised in the school gymnasium, each produced about 320 BTUs (British
Thermal Units) of heat. The gymnasium is 100 feet long, 80 feet wide, and 20 feet high.
How many BTUs per cubic foot did the students produce?
BTU/ft3
8. Approximately 175 chopped walnut pieces were stirred into a brownie mix that fills a 9”
diameter pan that is 1” deep. What is the density of the walnut pieces? How many walnut
pieces would you expect in a 2”  2”  1” brownie serving?
in3
= 2.75 pieces/in3 2.75(4) = 11 pieces
9. The clerk at the local pet store said, “Perfect aquarium density is when there are 1.5 gallons
of water for every 1 inch of fish.” An aquarium magazine has a photograph of a beautiful
aquarium with perfect density that contains 10 fish, each 3 inches long. What is the density
of the aquarium? How many gallons of water are in the aquarium in the photograph?
inch of fish/gallon
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30  0.66 = 45 gallons
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Part IV
10. You want to open a dog walking business, and are considering the east side of town and the
west side of town. You will open the business wherever the density of dogs per home is
greater than 0.35. According to town records, the dog population of the 20-city block east
side is 6 dogs per block with 18 homes per block. The dog population of the 30-city block
west side is 4 dogs per block with 10 homes per block. Where, if anywhere, should you open
your new dog walking business?
East Side of Town
West Side of Town
Number of
Dogs per Block
6
4
A. east side of town only
C. both east side and west side of town
Number of
Homes per Block
18
10
Number of
Dogs per Home
1/3 = 0.33
2/5 = 0.40
B. west side of town only
D. neither east side nor west side of town
11. While in the school library you notice some book sections seem to be more “crowded” with
regard to shelf space. Use the data provided by the librarian to determine the density of each
section of the school library.
Fiction
Non-Fiction
Reference
Number of
books
372
528
257
Total shelf space
in square feet
400
656
395
Density
(books/ft2)
0.930
0.804
0.650
30 threads
← 1 inch →
13. Thread count or TPI (threads per inch) is a measure of the coarseness or fineness of fabric. It
is the total number of vertical and horizontal threads in one square inch. It is measured by
counting the number of threads along two sides (across and up) of the square inch, added
together. It is usually used in regard to cotton linens such as bed sheets. Suppose you have a
bed sheet with a thread count of 60, this could mean there are 30 horizontal threads and 30
vertical threads per square inch as shown in the diagram.
Suppose you have a piece of cotton fabric that measures
36”  44” and has a total of 142,560 threads.
a. Determine the thread count (TPI) of the piece of cotton fabric.
← 1 inch →
30 threads
threads/in2
b. Estimate the number of threads on each of the two sides of one inch of the cotton fabric.
45 threads  45 threads
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www.cpalms.org