# Area of a Circle

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 cm2, 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 cm2 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)

= 28.26 in

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

8 cm = 2 ·

8 cm ÷ 2 =

= 4 cm

= 3.14 · (4 cm) · (4 cm)

= 50.24 cm

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

78.5 m = 3.14 · ·

78.5 m ÷ 3.14 · ·

25 m = ·

= 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? ANSWER BOX:   = cm  RESULTS BOX:
 2 The diameter of a circle is 12 inches. What is the area? ANSWER BOX:   = in  RESULTS BOX:
 3 The radius of a circular rug is 4 feet. What is the area? ANSWER BOX:   = ft  RESULTS BOX:
 4 The area of a coin is 3.14 square centimeters. What is the radius? ANSWER BOX:   = cm  RESULTS BOX:
 5 The diameter of a bicycle wheel is 20 inches. What is the area of the wheel? ANSWER BOX:   = in  RESULTS BOX:
 Circumference & Area Lessons Geometry and the Circle Circumference of a Circle Area of a Circle Practice Exercises Challenge Exercises Solutions