Year 8 Interactive Maths - Second Edition

Circumference

Activity 11.1

Equipment:  Compass, ruler, thread and calculator.
Purpose:  To find a formula for the circumference of a circle.

Step 1:  Use the compass to draw a circle.

Step 2:  Use the thread and ruler to measure the circumference, C, of the circle drawn.

Step 3:  Use the ruler to measure the diameter, d, of the circle.

Step 4:  Calculate the ratio C : d.  That is:

Activity 11.2

Step 1:  Use the compass to draw a larger circle than the one drawn in Activity 1.

Step 2:  Use the thread and ruler to measure the circumference, C, of the circle drawn.

Step 3:  Use the ruler to measure the diameter, d, of the circle.

Step 4:  Calculate the ratio C : d. That is:

In general:

For a circle of any size:

If r is the radius of the circle, then d = 2r.

Thus, the circumference, C, of a circle is given by:

Example 13

Find the circumference of a circle of diameter 63 cm using π = 3.14.

Solution:

So, the circumference of the circle is 197.82 cm.

Note:

To find the circumference of a circle, draw a diagram and label it.  Then write the formula
C = πd or C = 2πr.  Then substitute the given value of d or r and use a calculator to compute
the value of C.  Finally, state your answer in words.

Example 14

Find the circumference of a circle of radius 45 m using π = 3.14.

Solution:

So, the circumference of the circle is 282.6 m.

Key Terms

circumference