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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 Pi (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: C equals Pi times d. For simplicity, we use Pi = 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: diameter formula. spacediagram of the parts of a circle
circle with area shadedspace 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:
Area equals Pi times r squared space or space Area equals Pi times r times r
where Area is the area, and radius 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= 3.14 in our calculations.


Example 1: The radius of a circle is 3 inches. What is the area? diagram for example 1
Solution: Area equals Pi times r times r
  Area = 3.14 · (3 in) · (3 in)
  Area = 3.14 · (9 in2)
  Area = 28.26 in2

Example 2: The diameter of a circle is 8 centimeters. What is the area? diagram for example 2
Solution: diameter formula
  8 cm = 2 · radius
  8 cm ÷ 2 = radius
  radius = 4 cm
  Area equals Pi times r times r
  Area = 3.14 · (4 cm) · (4 cm)
  Area = 50.24 cm2

Example 3: The area of a circle is 78.5 square meters. What is the radius? diagram for example 3
Solution: Area equals Pi times r times r
  78.5 m2 = 3.14 · radius · radius
  78.5 m2 ÷ 3.14 = radius · radius
  25 m2 = radius · radius
  radius = 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:
diameter formula
Area equals Pi times r squared space or spaceArea equals Pi times r times r


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 = 3.14 to calculate your answers.

1.space The radius of a circle is 9 centimeters. What is the area?
ANSWER BOX:  Area = cm2

RESULTS BOX:


2.space The diameter of a circle is 12 inches. What is the area?
ANSWER BOX:  Area = in2

RESULTS BOX:


3.space The radius of a circular rug is 4 feet. What is the area?
ANSWER BOX:  Area = ft2

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 = in2

RESULTS BOX:



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

Circumference and Area Lessons
Geometry and the Circle
Circumference of a Circle
Area of a Circle
Practice Exercises
Challenge Exercises
Solutions

Related Activities
Circle Crosswords
Circle Solver
Circumference and String
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Pre-Made Worksheets

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