Title
Changes in the Circumference

Problem Statement
What happens to the circumference of a circle if you double the diameter?  If you triple the diameter?   If you halve the diameter?  As the diameter increases (or decreases) in measure, how does the circumference change?  Why does this change occur?

Problem setup

How does changing the diameter of a circle affect its circumference?

Plans to Solve/Investigate the Problem

Using Geometer’s Sketchpad, we look at the formula for the circumference of a circle C=2 p r or C = pd where p=3.14.  By changing the measure of the diameter of the circle, we can see the calculation changes in the circumference.

Investigation/Exploration of the Problem

We started with a circle (red) with a diameter equal to 1.0 inch (radius equal to .50 inch) and found that the circumference is 3.15 inches.  We next created a circle (black) with a diameter double the first, so that radius equals 1.0 inch and diameter equals 2.0 inches.  We found that the circumference also doubled. Next we created a circle (blue) with a diameter half the original circle, so that the diameter equals .50 and the circumference became 1.57. Next, we created a circle (green) with a diameter three times the original, so that the diameter equals 3.0 inches and the circumference became 9.42 inches; again approximately triple the original circumference of 3.15 inches.

The formula for the circumference of a circle is 2pr or pd.  Since p is approximately 3.14, the circumference is going to be approximately three times the diameter of any circle.

Extensions of the Problem

What happens to the area of a circle when its original diameter is doubled?  Tripled?