4.7 Volume

Mathematics

Perimeter, area and volume

Educator section

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

Leaner section

Content

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:

cubic mm : mm³

cubic cm : cm³

cubic m : m³

1 cm³ (cubic centimetre) is a cube with a length, breadth and height of 1 cm.

1 cm³ = 1 cm x 1 cm x 1 cm

= 10 mm x 10 mm x 10 mm

= 1 000 mm3

1 m³ = 1 m x 1 m x 1 m

= 100 cm x 100 cm x 100 cm

= 1 000 000 cm³

23.3 Also LEARN the following:

Volume of a rectangular prism is length x breadth x height

Volume of a cube is y³ y = (length, breadth and height)

23.4 Use the formula: volume = length x breadth x height

to calculate the volume of the following figures:

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b)

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c)

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23.5 a) Calculate the volume of the following in cm3:

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b) Calculate the volume of the following in mm3

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c) What is the volume of the figure in cm3?

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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 figure, e.g. a stone?

23.6.1 Did you know?

A Greek Mathematician, Archimedes, discovered how to calculate the volume of an irregular figure while he was bathing! He saw how water flowed 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 mℓ water you have in the cup!

b) Slowly lower the stone into the cup. Make certain that the water that overflows lands in the bigger container.

c) Measure the amount of water in the container by pouring it into a measuring cup.

d) Your stone has a volume of 1 cm3 for each mℓ of water that overflowed because 1 mℓ = 1 cm³.

e) What is the volume of your stone? .__________________________________

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.