Table 1.1: Prefixes of the basic units used in physics
Area and Volume in SI Units
In many of the numeric calculations that involve area or volume, the information given in the question describes area in cm2 or volume in cm3. Although all students are aware that there are 100 cm in 1 m, care must be taken to remember that there are 10 000 cm2 in 1 m2 and there are 1 000 000 cm3 in 1 m3. Consider the calculation of the area of a square: area length width. With a square of sides 1 m, the area is 1 m 1 m, which is clearly 1 m2. The same square can be described as having sides of length 100 cm; the area is now 100 cm 100 cm, which is equal to 10 000 cm2. Clearly 1 m2 10 000 cm2.A similar argument can be used to explain why 1 m3 1 000 000 cm3.
Proportionality
Two quantities are said to be proportional if they vary in such a way that one of the quantities is a constant multiple of the other. In other words, they increase or decrease together in a fixed ratio.
Directly Proportional
Two quantities, A and B, are ‘directly proportional’ to each other when the value of one is a constant multiple of the other. The symbol for ‘proportional to’ is ‘ ’.r
AN INTRODUCTION TO LEAVING CERT. PHYSICS 7
This row has 100 cubic centimetres in it
There are 100 slices altogether
The top slice therefore has 100 100 10 000 cubic centimetres in it
This row has 100 cubic centimetres in it
1 m
1 m
1 m
∴ there are (100)(10 000) cm3 in 1 m3 i.e. 1 m3 1 000 000 cm3 1 106 cm3 ⇒ 1 cm3 10–6 m3
Fig 1.1: Cube of sides length 1 m shows that 1 m3 1 000 000 cm3
