CC Geometry R
Name_____________________
Hwk. #13 Density
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1. A piece of copper with a volume of 8.25 cm has a mass of 73.92 grams.
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A piece of iron with a bolume of 5 cm has a mass of 39.35 grams.
Which metal has the greater density?
copper
iron
Copper: 73.92 Iron: 39.35
8.25
5
D = 8.96
D = 7.87
Copper has greater density.
2. A piece of metal with a density of 7.4 grams per cubic centimeter has a mass
of 90 grams. How many metal spheres with a radius of 1 centimeter could be
made out of this metal piece?
Volume(ball) = 4/3π(1)
= 4/3π
7.4 = 90
V
(12.162) ÷ (4/3π)
≈ 2.9035
V = 90 ≈ 12.162
7.4
Answer: 2
3. The United States has minted one-dollar silver coins called the American Eagle
Silver Bullion Coin since 1986. Each coin has a diameter of 40.6 mm. and is 2.98
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mm. thick. The density of silver is 10.5 grams per cm . What is the mass of an
American Eagle Silver Bullion Coin to the nearest gram?
Volume(coin) = π(2.03)2(.298)
= 3.858
diameter = 40.6 mm = 4.06 cm
height = 2.98 mm = 298 cm
D = M
V
10.5 = _M 3.858
Mass ≈ 41 g
4. Seawater contains approximately 1.2 ounces of salt per liter on average.
How many gallons of seawater, to the nearest tenth of a gallon, would
1 liter = 0.264 gallon
contain 1 pound of salt?
D = M
V
1.2 = 16
V
D = 1.2 Oz/liter m = 1 pound
Conversion m = 16 oz
V = 40/3 liters
40 (.264) = 3.5 Gallons
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1 gallon = 3.785 liters
1 pound = 16 oz
5. The density of the American white oak tree is 752 kilograms per cubic meter.
If the trunk of an American white oak tree has a circumference of 4.5 meters
and the height of the trunk is 8 meters,
what is the approximate number of kilograms of the trunk?
D = 752 kg/m3
C = 4.5 m
C = D
4.5 = D
V = r2 h
752 = m 12.884
D = 1.432
r = .716
V = (.716)2 8
V = 12.884
m= 9,688 Kilograms
6. A contractor needs to purchase 500 bricks. The dimensions of each brick
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are 5.1 cm by 10.2 cm by 20.3 cm, and the density of each brick is 1920 kg/m .
The maximum capacity of the contractor‛s trailer is 900 kg. Can the trailer
hold the weight of 500 bricks? Justify your answer.
.051 m X .102 m X .203 m = .001056 m3
1920 = x mass = 2.028 kg per brick
500 (2.028) = 1,014 kg
.001056
The trailer will not be able to carry all the bricks
Review:
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1. A sphere has a diameter of 4(x + 3) cm. and a surface area of 784π cm .
Find the value of x.
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2. A sphere is inscribed in a cube which has a volume of 64 in .
What is the surface area of the sphere, to the nearest tenth?
edge of cube = 4 in
radius of sphere = 2 in,
SA = 4πr2 = 4π(4) = 16π ≈ 50.3 in2