Copyright © Cengage Learning. All rights reserved. Functions 3 The Metric System

Copyright © Cengage Learning. All rights reserved. Volume and Area 3.4

3 Volume

4 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) Figure 3.10 One litre is a little more than 1 qt.

5 Volume The cubic metre (m 3 ) is used to measure large volumes. One cubic metre is the volume contained in a cube 1 m on an edge. The cubic centimetre (cm 3 ) is used to measure small volumes. It is the volume contained in a cube 1 cm on an edge.

6 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 (dm 3 ). That is, 1 L of liquid fills a cube 1 dm (10 cm) on an edge. (See Figure 3.11.) Figure 3.11 One litre contains 1000 cm 3.

7 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 cm 3 Thus, 1 L = 1000 cm 3. Note: (cm)(cm)(cm) = cm 3

8 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).

9 Volume The kilogram was defined as the mass of 1 dm 3 of water. Since 1 dm 3 = 1 L, 1 litre of water has a mass of 1 kg.

10 Example 1 Change 0.5 L to millilitres.

11 Area

12 Area A common unit of area in the metric system is the square metre (m 2 ), the area contained in a square whose sides are each 1 m long. The square centimetre (cm 2 ) and the square millimetre (mm 2 ) are smaller units of area. (See Figure 3.12.) The larger area units are the square kilometre (km 2 ) and the hectare (ha). Figure 3.12 Relative sizes of 1 cm 2 and 1 mm 2.

13 Example 3 Change 2400 cm 2 to m 2. 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.

14 Example 3 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. cont’d

15 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 m 2 or 1 square hectometre (hm 2 ). (See Figure 3.13.) Figure 3.13 Hectare

16 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.”