At what point will the circle and square have the same perimeter?
My process
My first guess was that the area of both shapes would be the same in the middle. My group and I used the number line to help us place it in the middle, so that we could measure the lengths on the projector. Placed at 20 inches, the length of one side on the square was 9.5 in. and the circumference of the circle was 12 in. From there we found the areas! Area of the Square: 90.25 in Area of the Circle: 113.4 in Unfortunately our first guess wasn't right on the dot but it was pretty close! Since the squares area was slightly smaller than the circle, we decided to |
move it over to the right so that the square's size would increase just a tad and the circle would decrease. So, we did the whole process all over again but placed at 21 inches on the number line.
Our outcome was:
Area of the Square: 100 in
Area of the Circle: 103.82 in
SO CLOSE, BUT SO FAR! Our last hypothesis for the day was that the areas will be the same somewhere in between 20 and 21.
Our outcome was:
Area of the Square: 100 in
Area of the Circle: 103.82 in
SO CLOSE, BUT SO FAR! Our last hypothesis for the day was that the areas will be the same somewhere in between 20 and 21.
These are two of my journal entries written about this problem
Other people's process
Since the process that my group and I's was tedious, we were pushed to create a formula what would make solving this problem a little cleaner and easier. I, myself struggle with coming up with formulas based on the data so I took a step back and watched other people's process. It was when the class came together that I started to understand how coming up with the formula works.
Above and Below are pictures of what we came up with
Once we simplified the formula, our teacher then taught us how to put the data into a graphing calculator. Here are pictures of our process!
The solution!
my self evaluation
Surprisingly, I actually really enjoyed this problem. I had a pretty good understanding of how the everything worked out. Hypothesis/Experimenting was definitely an important factor and surely a skill I practiced a ton in this process. I am proud to say that I feel like I deserve an A this time around. I tried hard and I was 100% involved throughout the entirety of this problem.