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Lesson Objectives
1. You will gain a deeper understanding of the fundamental concept of area of a circle.
2. You will understand how the formula for the area of a circle was determined.
3. You will demonstrate how to measure the area of a circle.
The Area of a CircleThe Area of a Circle
Developed byIvan Seneviratne
How in the world would you find the area of a circle?
The Area of a circle refers to the number of square units within the circle. Remember, area is always measured in square units.
Archimedes of Syracuse Calculating the area of a circle presented a
major problem for the mathematicians of Archimedes' time. Archimedes of Syracuse proved that the area of a circle was equal to multiplied by the square of the radius of the circle in “The Measurement of a Circle.”
Archimedes Screw,
Archimedes’ MethodImagine chopping up the circle as
if it were a pizza.
PRESTO!
Length
Height
So, What Now!To find the area of the circle
which is now a parallelogram, we just need to multiply the length by the Height.
Area = Length x Height
Wait a Minute! The height of this
“parallelogram” is really the radius of the circle. The length is really 1/2 of the circumference.
One half of circumference
Radius
Area = one half of circumference x Radius
Now What! The circumference is really x
Diameter and the diameter is twice the radius.
One half of circumference
Radius
Area = ½ x x Diameter x Radius
= ½ x x 2 x Radius x Radius
Area = x Radius x Radius = x r x r
= x r2
It’s As Easy As Pi!
Area of a Circle
The area of a circle is the region enclosed by the circle. It is given by the formula:
A = x r2
where A is the area and r is the radius.
Now Let’s Try This Formula
Find the area of this circle.
5 cm
Now Let’s Try Again
Find the area of this circle.
10 cm
This presentation is developed by Ivan Seneviratne © 2007 purely for personal use.
