*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. 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 the formula c= π d. C1 = (2d)π =2 so C1=2C

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GSP file

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?

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GSP file

Looking
at the formula for area (A= πr^{2}) then A=π(2r)^{2} which therefore would be same as π4r^{2}.
When you double the diameter of the circle then the area also doubles and
tripling the diameter also triples the area.

*Author & Contact*

Jill Jackson and Shirley Crawford

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*Link(s) to resources, references, lesson plans, and/or other materials*

Link 1

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