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 Geometerís 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 withthe formula c= π d.†† C1 = (2d)π =2 so C1=2C

 

 

Click here to see 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?

 

Click here to see GSP file

 

 

Looking at the formula for area (A= πr2) then A=π(2r)2which therefore would be same as π4r2. 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
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