
Area of a
Circle 

Unit 2
> Lesson 3 of 6 
The distance around a
circle
is called its circumference. The distance across a circle through its center
is called its diameter. We use the Greek letter
(pronounced Pi) to
represent the ratio of the circumference of a circle to the diameter. In the last lesson, we learned that
the formula for circumference of a circle is:
. For simplicity, we
use = 3.14.
We know from the last lesson that the diameter of a circle is twice as long as the
radius.
This relationship is expressed in the following formula:
.



The area of a circle is the number of square units inside that circle. If each square in the circle to the left has an area
of 1 cm^{2}, you could count the total number of squares to get the area of this circle. Thus, if there were a total of
28.26 squares, the area of this circle would be 28.26 cm^{2} However, it is easier to use
one of the following formulas:

or

where is the area, and
is the radius. Let's look at some examples involving the area of a circle. In each of the three examples below, we will
use = 3.14 in our calculations.

Example 1: 
The radius of a circle is 3 inches. What is the area?


Solution: 


= 3.14 · (3 in) · (3 in) 

= 3.14 · (9 in^{2}) 

= 28.26 in^{2} 

Example 2: 
The diameter of a circle is 8 centimeters. What is the area?


Solution: 


8 cm = 2 ·


8 cm ÷ 2 =


= 4 cm 



= 3.14 · (4 cm) · (4 cm) 

= 50.24 cm^{2} 

Example 3: 
The area of a circle is 78.5 square meters. What is the radius?


Solution: 


78.5 m^{2} = 3.14 ·
·


78.5 m^{2} ÷ 3.14 =
·


25 m^{2} =
·


= 5 m 
Summary: 
Given the radius or diameter of a circle, we can find its area. We can
also find the radius (and diameter) of a circle given its area. The formulas for the diameter and area of a circle are listed below:




or

Exercises
Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER.
After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect.
To start over, click CLEAR. Use
= 3.14 to
calculate your answers. 
1.

The radius of a circle is 9 centimeters. What is the area?

2.

The diameter of a circle is 12 inches. What is the area?

3.

The radius of a circular rug is 4 feet. What is the area?

4.

The area of a coin is 3.14 square centimeters. What is the radius?

5.

The diameter of a bicycle wheel is 20 inches. What is the area of the wheel?

This lesson is by Gisele Glosser. You can find me on Google.
