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.**

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