- circle is a round, two dimensional shape that looks similar to the letter ‘O’.
- In strict mathematical language, circle refers to the boundary of the shape while ‘disk’ is used to refer to the whole shape, including the inside.
- A straight line from the center of a circle to the edge is called the radius.
- A straight line that passes from one side of a circle to the other through the center is called the diameter.
- The distance around the outside of a circle is called the circumference.
- All points on the edge of a circle are the same distance to the center.
- The value of Pi (π ) to 2 decimal places is 3.14, it comes in handy when working out the circumference and area of a circle.
- The circumference of a circle can be found with the following formula: Circumference = π d
- The area of a circle can be found with the following formula: Area = π r²
- An arc is part of the circumference of a circle.
- A chord is a straight line joining two points on a circle, the diameter is an example of a chord (the longest possible one).
- A segment is the region between a chord and the arc it joins.
- A tangent is a straight line that touches a single point of a circle.
- A sector is the region between an arc and two radii.
- The full arc of a circle measures 360 degrees.
- A semicircle is a shape that forms half a circle, the arc of a semicircle measures 180 degrees.
- Circles have a high level of symmetry.
- A circle has the shortest perimeter of all shapes with the same area.
- The circle shape is a favorite of humans and can be seen in many designs.
- The invention of the wheel (a circle shape) was one of the most important in human history.

Area of a Circle

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,

Example 8

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 9Find the area of a circle of whose diameter is 11 cm using

Solution:

So, the area is 94.99 cm2.

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

Purpose:Purpose:

**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 30º around the circle.**Step 3:**Using a ruler and a pencil, draw lines joining each 30º 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 9Find 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.