OpenStax-CNX module: m22161
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Volume
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†
Creative Commons Attribution License 3.0
1 MATHEMATICS
2 Perimeter, Area and Volume
3 EDUCATOR SECTION
4 Memorandum
23.4
a) 108 cubic cm
b) 72 cubic cm
c) 23,625 cubic cm
d) 108 cubic cm
23.5
a) 20 cubic cm
b) 63 000 cubic mm
c) 24 000 cubic cm
d) 1 728 cubic cm
e) own answer
5 LEANER SECTION
6 Content
6.1 ACTIVITY: Volume [LO 4.2, LO 4.3]
23. VOLUME
23.1 Did you know?
The amount of space that is taken up by a solid body is called the volume of the body.
The internal volume is thus the space inside a hollow container. It is also called the capacity or contents
of the container.
23.2 IMPORTANT to REMEMBER!
Volume is measured in cubic measuring units
We use the following units:
3
cubic mm : mm
3
cubic cm : cm
∗ Version
1.1: Apr 20, 2009 12:37 am -0500
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OpenStax-CNX module: m22161
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3
cubic m : m
1 cm
3
(cubic centimetre) is a cube with a length, breadth and height of 1 cm.
1 cm
3
= 1 cm x 1 cm x 1 cm
= 10 mm x 10 mm x 10 mm
= 1 000 mm3
1 m
3
= 1 m x 1 m x 1 m
= 100 cm x 100 cm x 100 cm
3
= 1 000 000 cm
23.3 Also LEARN the following:
Volume of a rectangular prism is length x breadth x height
Volume of a cube is y
3
y = (length, breadth and height)
23.4 Use the formula: volume = length x breadth x height
to calculate the volume of the following gures:
Figure 1
a)
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b)
Figure 2
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c)
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Figure 3
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Figure 4
d)
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23.5 a) Calculate the volume of the following in cm3:
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Figure 5
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b) Calculate the volume of the following in mm3
Figure 6
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c) What is the volume of the gure in cm3?
Figure 7
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OpenStax-CNX module: m22161
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d) Calculate the volume of a cube with a length of 12 cm.
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e) Estimate the volume of the box of chalk in your classroom
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23.6 CLASS DISCUSSION
How will you determine the volume of an irregular gure, e.g. a stone?
23.6.1 Did you know?
A Greek Mathematician, Archimedes, discovered how to calculate the volume of an irregular gure while
he was bathing! He saw how water owed over the edge of the bath when he climbed in. He realised that
if he could measure the volume of water that his body displaced, then he could measure the volume of his
own body. Archimedes was so excited by this realisation that he jumped out of the bath and ran down the
street stark naked shouting, EUREKA! (I have found it!)
23.6.2 Follow the following steps and see if you can measure the volume of a stone that you have picked
up outside.
a) Fill a cup completely to the top with water and put the cup in a bigger container. Remember to see
precisely how many m` water you have in the cup!
b) Slowly lower the stone into the cup. Make certain that the water that overows lands in the bigger
container.
c) Measure the amount of water in the container by pouring it into a measuring cup.
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d) Your stone has a volume of 1 cm3 for each m` of water that overowed because 1 m` = 1 cm .
e) What is the volume of your stone? .__________________________________
7 Assessment
Learning Outcome 4: The learner will be able to use appropriate measuring units, instruments and formulae
in a variety of contexts.
Assessment Standard 4.2: We know this when the learner solves problems;
Assessment Standard 4.3: We know this when the learner solves problems using a range of strategies.
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