Units of Area and Volume

The unit of area is the square meter(m 2), which represents the area of a square of side 1 m; the unit of volume is the cubic meter (m 3), equal to the volume of a cube of side 1 m. In order to avoid exceedingly small or large numerical values in the computation of areas and volumes, one uses systems of subunits obtained by respectively squaring and cubing not only the millimeter but also two intermediate submultiples of the meter, namely, the  decimeter(dm) and the centimeter(cm). Since, by definition,  and the submultiples of the unit of volume are

                                                                        

It should be noted that when the volume of a liquid is being measured, the cubic decimeter (dm 3) is usually referred to as a liter (L). 

 

Other derived SI units used to measure the moment of a force, the work of a force, etc., are shown in Table 1.2 . While these units will be introduced in later chapters as they are needed, we should note an important rule at this time: When a derived unit is obtained by dividing a base unit by another base unit, a prefix may be used in the numerator of the derived unit but not in its denominator. For example, the constant kof a spring which stretches 20 mm under a load of 100 N will be expressed as 

but never as k 55 N/mm.