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 of the circle?
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 of the circle?
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 of the circle?
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 of the circle? |
2. | The diameter of a circle is 12 inches. What is the area of the circle? |
3. | The radius of a circular rug is 4 feet. What is the area of the circle? |
4. | The area of a coin is 3.14 square centimeters. What is the radius of the circle? |
5. | The diameter of a bicycle wheel is 20 inches. What is the area of the wheel? |