Displacement and Density
Section 10.5
April 12, 2005
Answers to Homework
Page 543:
6. 3456
12. r = 9 in.
16. The golf ball is 10.6; the volume left in the
cylinder is 16; so the water will not overflow.
Page 547
5. V = 256/3   85.3 
6. S.A. = 144 .
Displacement
• What happens when I add ice cubes to a glass
of soda? What happens when you put a scoop
of ice cream in some root beer? What happens
if you put your dog in the tub full of water for a
bath?
• All of these are examples of DISPLACEMENT,
which means that the water is displaced by an
object when it is placed in water.
Displacement
• You can use displacement to find the volume of
any object, especially objects of irregular size
that we cannot measure with a formula.
• We just have to put them in an object filled with
water in a container we can find the volume of!
DEMONSTRATION
Find the volume of the rock.
• Volume of water in square prism BEFORE
inserting rock:
– V = BH = (4 in)(4 in)(____) =
• Volume of water AFTER:
– V = BH = (4 in)(4 in)(____) =
• What is the volume of the water DISPLACED?
– Vafter – Vbefore = _____
• What is the volume of the rock? _____
Find the volume of the object.
• Volume of water in cylindrical container BEFORE
inserting object:
– V = BH = r2H = (2 in)2(____) = _______
• Volume of water AFTER:
– V = r2H = (2 in)2(____) = _______ =
• What is the volume of the water DISPLACED?
–
Vafter – Vbefore = _____
• What is the volume of the object?
• What is another way to find the displaced volume?
What changes as you insert the object?
So to find the volume using
displacement:
V = BH where B is the area of the base of the container
(prism or cylinder) and H is the change in the height of
the water.
Example: When you place a clump of metal into a
container of water, it raises that water level by 5 cm. If
the container is a rectangular prism whose base
measures 15 cm by 15 cm, what is the volume of the
metal?
Archimedes, Again!
Silver's
A king once
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and
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It should
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mixed silver
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The kind
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harm
whether
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gold
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Now, you
of a
know
crown?
that all he had
to do was to figure out the
density of the metal.
Finding Density
• Density is the mass of matter in a given volume.
• Density is the ratio of the mass of a substance to
its volume, and it can be calculated by dividing
the mass by the volume. Density is often
expressed in units such as grams per cubic
centimeter (g/cm3) or pounds per cubic foot
(lb/ft3).
• Density = Mass / Volume
Density Table
Metal
Density
Metal
Density
Aluminum
2.81 g/cm3
Nickel
8.89 g/cm3
Copper
8.97 g/cm3
Platinum
21.40 g/cm3
Gold
19.30 g/cm3
Potassium
0.86 g/cm3
Lead
11.30 g/cm3
Silver
10.50 g/cm3
Lithium
0.54 g/cm3
Sodium
0.97 g/cm3
Calculating Density
• Archimedes places the crown in a cylindrical
container full of water of radius 6 cm, and
notices that the water level rises 1.1 cm. He
weighs the crown and notices that it weighs
2401.05 grams. Is the crown made of gold?
– Mass = 2401.05 g
– Volume = V = r2H = (6 cm)2(1.1 cm) = _______
– Density = Mass / Volume = __________
Homework
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