Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

2.2 Using π (pi)

If you could measure these objects more accurately, you would find that the circumference divided by the diameter always gives the same answer. This value is known as ‘pi’ (pronounced ‘pie’) and it is denoted by the Greek letter pi. The value of pi is approximately 3.142, although for most calculations you will be using the pi button on your calculator, which shows pi to many more decimal places.

In fact, pi is an irrational number. This means that it can’t be represented exactly as a fraction and has an infinite number of decimal places, with no repeating pattern of numbers.

This knowledge that the circumference divided by the diameter for any circle gives a constant value of around 3.142 enables a formula to calculate the circumference from the diameter or the radius of a circle to be formed. Therefore:

circumference equals pi multiplication diameter or c equals pi multiplication d

Because the diameter is twice the radius, this can also be written as:

circumference equals pi multiplication diameter or c equals two multiplication pi multiplication r

You will now be asked to select the relevant formula to use in the next activity.

Activity _unit7.2.3 Activity 4 Circumference of a circle

Timing: Allow approximately 5 minutes

Suppose a circular table has a diameter of 1.5 metres. How many people can sit down comfortably for a meal at the table, assuming that each person requires a space of about 0.75 m? Use the button marked with π on your calculator. If you need a hint or tip simply click on ‘reveal comment’.

Figure _unit7.2.3 Figure 14 Diagram of a circular table with a 1.5 m diameter

Discussion

If you want some help to visualise the problem you could draw a quick sketch of the table and gaps for each person.

Answer

To see how many people will fit comfortably around the table you need to first work out the circumference of the table.

The diameter is given, so the circumference can be found with the formula:

multiline equation line 1 circumference equals pi multiplication diameter line 2 equation left hand side equals right hand side pi multiplication 1.5 m line 3 equals 4.7 m left parenthesis to one decimal place right parenthesis

Each person needs a space of about 0.75 m in width.

multiline equation line 1 Number of people who can fit around the table equals 4.7 m prefix division of 0.75 m line 2 almost equals six left parenthesis almost equals means approximately equal to right parenthesis

Therefore, six people should be able to fit around the table.

More often than not, the shape of which you need to know the perimeter will not be a simple circle, or rectangle. So, what do you do then? You’ll find out in the next short section.

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