# CIRCLES PART 1

by Ms. B. L. Norton

This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

The purpose of this lesson is to introduce students to calculations associated with circles and applying those calculations to various sized circles.

Do you know what a circle is ???

A circle is a shape in which all its points are the same distance for the center.

Can you think of some objects that are shaped like circles?

( hint :        )

Before we start, let's take a look at some "circular" terms.

The point located in the center of the circle is called the origin. Notice that the circle has a letter in the inside next to the center.  This letter names the circle.  In my example given, the circle will be called "circle B".

If I picked a point on the circle and drew a line from that point to the center of the circle, that would create a line of  radius (r).  Similarly, If I drew a line from the center of the circle to another point on the circle, that would also create a radius.

Notice that I now have two (2) radii ( pronounced ray-dee-eye), which is the plural form of the word radius.

I  have just created another part of a circle called the diameter (d).  The diameter is a straight line which originates at a point on the circle, passes through the center point or origin of the circle, and ends at a point on the opposite end of the circle.

The distance around a circle is called the circumference (C).

There is a relationship that exists between the circumference and the diameter.  If you know the measurement of the circumference and divide it by the diameter, there is a constant number derived that we call Pi.

This is the symbol for Pi...

Pi is equivalent to 3.1459265898....

Let's use 3.14 or 22/7 to represent Pi.  (that's easier to remember and work with.)

What does the Energizer bunny and the number Pi have in common? (Hint: click here )

click inside the circle for the answer !

The formula for calculating the circumference of a circle is:  C= pd  or C=2rp

If you know the diameter, then you can calculate the radius by dividing the diameter in half :  r = d/2

Similarly, if you know the radius, then you can calculate the diameter by multiplying the radius by 2:  d = r x 2

Let's do some examples:

 Problem Solution C= 34.54 meters      What is the diameter? Divide the diameter by p. d= C/p 34.54 meters / 3.14 = 11 meters r = 2 cm    What is the Circumference? Step 1.  Multiply the radius (r) by 2 to calculate the diameter. d = r x 2 d = 2 cm x 2 = 4 cm Step 2. Multiply the diameter by p to calculate the circumference. C= d x p C= 4cm x 3.14 = 12.56 cm d= 32 in.    What is the Circumference? Multiply the diameter by p to calculate the Circumference C = d x p C= 32 in. x 3.14 =   100.48 in.

WEB QUEST (ready for some p trivia?)

Directions:    Use the hyperlinks to search the sites for  answers to these questions:

Around what year was pi known to be equivalent to 3 ?    Pi can be calculated to how many places?

Can you write pi to more than 15 decimal places?

Eratosthenes was the first to do what  (in relation to circumference)?

Use the links on this website to find something interesting about pi to share with the class: http://www.pithemovie.com/gifpage.html

What are crop circles? (Don't forget to look at the pictures - 1, 2, and 3 !)

Use this search engine to find the circumference of the earth:    www.dogpile.com

Take the circumference quiz !