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.


_
at

1 comment:

  1. Kevin KimOctober 4, 2011 at 6:50:00 AM GMT+9

    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.

    ReplyDelete

READ THIS BEFORE COMMENTING!

All comments are subject to approval before they are published, so they will not appear immediately. Comments should be civil, relevant, and substantive. Anonymous comments are not allowed and will be unceremoniously deleted. For more on my comments policy, please see this entry on my other blog.

AND A NEW RULE (per this post): comments critical of Trump's lying must include criticism of Biden's or Kamala's or some prominent leftie's lying on a one-for-one basis! Failure to be balanced means your comment will not be published.