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Circle Problems - DMS Discussion

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Circle Problems - DMS Discussion
by ZIML Admin - Wednesday, November 15, 2017, 11:34 AM

From the week of November 6 to November 10 we chose Monday's problem (that you can find here):

In the diagram below, the large circle has radius $4$


What is the shaded area? Use $\pi=3.14$ and round your answer to the nearest integer..

17% of the students who tried the problem got it right on their first attempt.

The problem is asking us to find the area of a shape that, at first, may seem "odd". However, we can cut an paste some parts of the shaded region to make it into a shape that for which the area is a lot easier to find. There are several ways to do so. Adding extra lines to the drawing usually helps.

Take a look at the same diagram, but now with some inscribed squares inside each of the small circles: 


Note how now we can see some parts of the shaded region can be moved around to form a circle with a square removed in the middle. 


In these diagrams the shaded region did not change area, but in the last diagram it is easier to calculate. Now that we see the shaded region is the same as the area of a circle minus a square, what can we need to do to find it?

Share your thoughts and questions below!