This week's MGRE Math Beast challenge is actually a much easier version of the problem that I and a student collaboratively created a few weeks back.
The Math Beast roars:
In the figure above, a circle with radius 2 is inscribed in a square. What is the area of the shaded region?
(A) –2π + 16
(B) –π + 4
(C) 2π + 8
(D) 4π
(E) 8π – 2
If you were able to get through my problem, this problem will be a piece of cake. Check the comment section for my answer after you've had a go at the problem.
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1 comment:
Spoiler alert! as they say.
Here's how I arrived at my answer to this problem.
We know the circle is inscribed inside the square and has a radius of 2.
We thus know the circle has a diameter of 4, and by extension, the square's sides have a length of 4.
As a result, we know that
1. Area(square) = 16
2. Area(circle) = 4π
The area of the four corners must therefore be 16 - 4π. The area of only two of the four corners is thus:
8 - 2π.
The area of two corners plus the circle is therefore
(8 - 2π) + 4π,
which works out to
8 + 2π.
The answer is (C), 2π + 8.
QED.
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