# Changes in Circumference

By

Scottie Benford

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?

To be able to make conclusions about this investigation I’m planning on using a circle with a diameter of ten units.  I will be able to use  ten as my standard.   Then I will follow the instructions in my investigation, double the length, triple the length, and half the length.  I will use the grid on GSP and plot points so my diameter measurements will be exact.

This is the circle that I will use as a standard.  I used the plotting tool on the grid to get a radius of five so my diameter would be ten.  My circumference is 31.42 cm.

When my diameter is doubled to 20 cm. My circumference of the circle doubles as well.  The ratio of 31.42 to 62.83 = 1to 2 our double.

I cut my diameter in half by making it equal 5cm.  The circumference is 15.71 cm., which is half of my standard.  So far the relationship of what I do to my diameter is the same as what happens to my circumference.  I’m concluding that the reason this is true because there is a constant involved in my problem.  I can take each circumference of the circles and divide by my diameter and I always get pi.  For those who have more understanding of equations you could look at this problem like an equation.  If you have 5x and x=2 your answer would be 10.  Let’s leave x as a constant and change 5 to 10, 10x=20.   You can see the answer doubles, just as our circumference did when the diameter doubles.