5.3 Circumferences and Areas of a Circle


Holt, Rinehart, and Winston



* Identify and apply formulas for the circumference and area of a circle.

* Solve problems using the formulas for the circumference and area of a circle.


The Definition of a Circle:

Let us review the parts of a circle.

A circle is a set of points in a plane that aar eequal distance, r (radius), from a given point in the plane known as the center (C) of the circle. The distance d = 2r is known as the diameter of the circle.


Circumference of a Circle:

By the time students enter a geometry classroom, they have used circumference and area. They were given formulas and were taught to apply those formulas to a set of numbers. In this text, the students are geared to look at the circumference in relationship to "pie and area in relationship objects already studied..

Definition: The circumference of a circle is the distance around the circle. The circumference of a circle, C, with diameter, d, and radius, r, is given by:

Now look at three different circles:

On average the ratio of the three circles is

(3.13951+3.1352+3.14)/3 = 3.13824

The more circles there are the more the ratio of C/d will converge to 3.14.


Here is a brief history of Pi from Wolfram Research website.



Area of a Circle:


The area, A, of a circle with radius, r, is given by:




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