By the end of this section you should: ● understand how to fi nd the circumference of a circle ● understand what a disc is ● understand how to fi nd the area of a disc
Discuss and discover
While working with a partner, use a compass and ruler to draw circles with the measurements shown in the table below.
Using a piece of string and a ruler, measure the length of the circle (this is called the circumference). Copy the table and fi ll in the missing values.
Radius Diameter Circumference Circumference
3 cm 5 cm 5·8 cm 64 mm
What have you discovered about the values in your last column?
Length of a circle
The circumference is the length of the circle if it were opened up and straightened out to a line segment. This was the length of the string that fi t exactly around each circle in the activity above.
The length of a whole circle is called its circumference.
From the activity above, you should have discovered that the values in the last column were approximately the same in each case. This value is a special number called pi, represented by the symbol π .
π = circumference
___________ diameter
π is a letter in the Greek alphabet called ‘pi’.
Circumference
π is a constant value for all circles. The approximate values we use include 3·14 and 22 using the π button on the calculator.
__ 7 , or by
π is an irrational number, which is a real number that cannot be written as a simple fraction. This is why we use approximate values for π .
Circumference comes from the Latin circumferens, meaning ‘carrying around’.