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Succeed with maths: part 2
Succeed with maths: part 2

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2.1 Perimeters of circles

As you saw earlier in this week, the perimeter of the circle has its own name: the circumference. But is there an easy way to calculate the circumference of a circle as there is with a rectangle?

Let’s investigate this in the following practical activity. For this you will need a tape measure (or a piece of string and a ruler) and five objects such as mugs, cans, bowls or buckets that have a circular top or bottom.

Activity 3 Circles

Timing: Allow approximately 15 minutes

Measure the circumference and diameter of each object in centimetres to the nearest 0.1 cm (or 1 mm). Use the tape measure (or string and ruler) to find the circumference and the ruler to find the diameter.

Write down the diameter and the circumference of each object in a table and calculate the ratio circumference divided by diameter. What do you notice about your answers?

Answer

Here are some results that were obtained when carrying out the activity. The important data to consider are the ratios between the circumferences and the diameters.

Some sample results:

Table 1 Sample measurements of circular-shaped kitchen items
ItemDiameter (in cm)Circumference (in cm)circumference divided by diameter (rounded to 1 decimal place)
Spice jar4.414.13.2
Drinking glass6.620.93.2
Tin container8.6273.1
Mug10.332.33.1
Bowl23.072.83.2

It is difficult to measure these quantities accurately. However, it is noticeable that in each case, the ratio of the circumference to the diameter seems to be about 3.1 or 3.2. In other words, the circumference is just over three times the length of the diameter.