Tuesday, October 04, 2011

MGRE's Math Beast Challenge problem this week

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.


1 comment:

Kevin Kim said...

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.