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Year 8 Interactive Maths - Second Edition


Area of a Circle

Activity 12.1

Equipment:  You will need a compass, pair of scissors, ruler and protractor for this activity.
Purpose: 
To discover a formula for the area of a circle.

Step 1:  Using the compass, draw a circle of radius 7 cm.  Then mark the circle's centre and draw its radius.

Step 2:  Place the centre of the protractor at the centre of the circle and the zero line along the radius. Then mark every 30 around the circle.

Step 3:  Using a ruler and a pencil, draw lines joining each 30 mark to the centre of the circle to form 6 diameters.  The diagram thus obtained will have 12 parts as shown below.

Step 4:  Colour the parts as shown below.

Step 5:  Cut out the circle and then cut along the diameters so that all parts (i.e. sectors) are separated.

Step 6:  Arrange all of the sectors to make a shape that approximates a parallelogram as shown below.

Step 7:  Using a ruler, measure the base and the height of the approximate parallelogram obtained in Step 6.


Questions:

1.  Calculate the area of the figure in Step 6 by using the formula:

2.  What is the area of the circle drawn in Step 1?

3.  It appears that there is a formula for calculating the area of a circle.  Can you discover it?


Formula for the Area of a Circle

From the above activity, it is clear that by arranging the sectors of the circle as a parallelogram that:


Remember:

The area, A, of a circle is given by the following formula where r is the radius of the circle:


Example 8

Solution:

So, the area is 616 m2.


Note:

To find the area of a region enclosed within a plane figure, draw a diagram and write an appropriate formula.  Then substitute the given values and use a calculator, if necessary, to obtain the required area.


Example 9

Find the area of a circle of whose diameter is 11 cm using π = 3.14.  Round your answer to 2 decimal places.

Solution:

So, the area is 94.99 cm2.


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