# Is there enough info to do this problem?

• Jul 30th 2010, 09:00 AM
sfspitfire23
Is there enough info to do this problem?
Given a figure of a square with a circle inscribed in it. If the area of the shaded region (the region outside of the inscribed circle) is 1, then find the area of the circle?

A. pi/4
B. pi
C. pi/(pi-4)
D.1/2(pi-4)
E. pi/(pi-4)^2

This is a gre quant Q
• Jul 30th 2010, 09:16 AM
Unknown008
Let's say the side of the square is x. Then, the shaded area is given by:

$x^2 - \pi (\frac{x}{2})^2 = 1$

Solve for x. Then find the area of the square (Happy)
• Jul 30th 2010, 09:38 AM
sfspitfire23
I'm trying to use (2r)^2 as the area of my square but the answer won't come out that way. Why is this?
• Jul 30th 2010, 09:47 AM
Unknown008
Oops, typo from my part. You need to find the area of the circle... not the square. Sorry (Itwasntme)

Ok, $x^2 - \pi (\frac{x}{2})^2 = 1$

So,

$x^2(1-\frac{\pi}{4}) = 1$

For ease, I'll multiply by pi and 1/4.

$\frac{x^2\pi}{4}(1-\frac{\pi}{4}) = \frac{\pi}{4}$

$\frac{x^2\pi}{4} = \frac{\pi}{4(1-\frac{\pi}{4})}$

But x^2/4 * pi is the area of the circle... so;

$Area = \frac{\pi}{4-\pi}$

Simplify if need be.
• Jul 30th 2010, 10:35 AM
Wilmer
Quote:

Originally Posted by sfspitfire23
I'm trying to use (2r)^2 as the area of my square but the answer won't come out that way. Why is this?

Should come out ok:
4r^2 - pi r^2 = 1
r^2(4 - pi) = 1
Hokay?