Area of a Circle
Circle are simple closed curves which divide the plane into two regions, an interior and an exterior.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: . 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: d = 2 * r
Purpose: To discover a formula for the area of a 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: A = PI * r * r
where "A" is the area, and "r" 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:
A = 3.14 · (3 in) · (3 in)
A = 3.14 · (9 in2)
A = 28.26 in2
Example 2: The diameter of a circle is 8 centimeters. What is the area?
Solution:
8 cm = 2 * r
8 cm ÷ 2 = r
r = 4 cm
A = 3.14 · (4 cm) · (4 cm)
A = 50.24 cm2
What did we find? We can understand why Pi is less than 4 and furtherconsideration will help someone see why it is greater than 3. Take alook at this investigation again and then see if you can estimate thearea of circle with any radius.
Sometimes a different point of view is all you need to make a connection to a concept.
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