Area of a Circle

Area of a Circle

circle partsThe 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 pi.gif (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: circum_formula.gif. For simplicity, we use pi.gif = 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: diam_formula.gif.

circle gridThe 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:

area_formula.gif or area_formula2.gif

where a_0.gif is the area, and r.gif 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 pi.gif= 3.14 in our calculations.


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

circleSolution:

area_formula2.gif

a_0.gif = 3.14 · (3 in) · (3 in)

a_0.gif = 3.14 · (9 in)

a_0.gif = 28.26 in


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

diam_formula.gif

8 cm = 2 · r.gif

8 cm ÷ 2 = r.gif

r.gif = 4 cm

area_formula2.gif

a_0.gif = 3.14 · (4 cm) · (4 cm)

a_0.gif = 50.24 cm


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

area_formula2.gif

78.5 m = 3.14 · r.gif· r.gif

78.5 m ÷ 3.14 · r.gif· r.gif

25 m = r.gif· r.gif

r.gif = 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:

diam_formula.gif

area_formula.gif or area_formula2.gif


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 pi.gif = 3.14 to calculate your answers.

 

1.space The radius of a circle is 9 centimeters. What is the area?
ANSWER BOX:  Area = cm  

RESULTS BOX: 

2.space The diameter of a circle is 12 inches. What is the area?
ANSWER BOX:  Area = in  

RESULTS BOX: 

3.space The radius of a circular rug is 4 feet. What is the area?
ANSWER BOX:  Area = ft  

RESULTS BOX: 

4.space The area of a coin is 3.14 square centimeters. What is the radius?
ANSWER BOX:  radius = cm  

RESULTS BOX: 

5.space The diameter of a bicycle wheel is 20 inches. What is the area of the wheel?
ANSWER BOX:  Area = in  

RESULTS BOX: