3
The Metric System
Functions
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3.4
Volume and Area
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Volume
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Volume
A common unit of volume in the metric system is the litre
(L). One litre of milk is a little more than 1 quart. The litre is
commonly used for liquid volume. (See Figure 3.10.)
(a)
(b)
One litre is a little more than 1 qt.
Figure 3.10
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Volume
The cubic metre (m3) is used to measure large volumes.
One cubic metre is the volume contained in a cube 1 m on
an edge.
The cubic centimetre (cm3) is used to measure small
volumes. It is the volume contained in a cube 1 cm on an
edge.
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Volume
Note:
It is important to understand the relationship between the
litre and the cubic centimetre.
The litre is defined as the
volume in 1 cubic decimetre
(dm3). That is, 1 L of liquid
fills a cube 1 dm (10 cm) on
an edge. (See Figure 3.11.)
One litre contains 1000 cm3.
Figure 3.11
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Volume
The volume of the cube in Figure 3.11 can also be found by
the formula
V = lwh
V = (10 cm)(10 cm)(10 cm)
= 1000 cm3
Note: (cm)(cm)(cm) = cm3
Thus, 1 L = 1000 cm3.
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Volume
Dividing each side by 1000, we have
or
Milk, soft drinks, and gasoline are sold by the litre. Liquid
medicine and eye drops are sold by the millilitre. Large
quantities of liquid are sold by the kilolitre (1000 L).
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Volume
The kilogram was defined as the mass of 1 dm3 of water.
Since 1 dm3 = 1 L, 1 litre of water has a mass of 1 kg.
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Example 1
Change 0.5 L to millilitres.
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Area
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Area
A common unit of area in the metric system is the square
metre (m2), the area contained in a square whose sides
are each 1 m long.
The square centimetre (cm2) and
the square millimetre (mm2) are
smaller units of area. (See
Figure 3.12.) The larger area
units are the square kilometre
Relative sizes of 1 cm2 and 1 mm2.
Figure 3.12
(km2) and the hectare (ha).
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Example 3
Change 2400 cm2 to m2.
Use the length conversion factor 1 m = 100 cm and first
form the conversion factor with cm in the denominator and
m in the numerator.
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Example 3
cont’d
Then raise the conversion factor to the second power to
obtain square units in both numerator and denominator.
Since the numerator equals the denominator, both the
length conversion factor
and its second power
equal 1.
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Area
The hectare (ha) is the basic metric unit of land area.
The area of 1 hectare equals the area of a square 100 m
on a side, whose area is 10,000 m2 or 1 square hectometre
(hm2). (See Figure 3.13.)
Hectare
Figure 3.13
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Area
The hectare is used because it is more convenient to say
and use than “square hectometre.”
The metric prefixes are not used with the hectare unit.
Instead of saying the prefix “kilo” with “hectare,” we say
“1000 hectares.”
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