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by [email protected] » Fri Oct 10, 2014 1:32 pm
Hi kamalakarthi,

In these types of multi-shape questions, it's usually a must to focus on the radius of the circle. Do you know it's value? Can you figure it out? How does the radius "interact" with the other shape(s)?

Here, we know that the area of the square is 16, so each side of the square = 4.

The diagonal of the square = the diameter of the circle. So....

4(root2) = diameter
2(root2) = radius

Next, plug the radius into the formula for area of a circle: pi(radius)^2

pi(2root2)^2 = 8pi

Final Answer: C

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by Brent@GMATPrepNow » Fri Oct 10, 2014 6:54 pm
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In the figure above, a square is inscribed in a circle. If the area of the inscribed square is 16 units, what is the area of the circular region ?

A) 2pi
B) 4pi
C) 8pi
D) 12pi
E) 16pi
IMPORTANT: the diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.
We can use this fact to solve the question by simply "eyeballing" the diagram.

NOTICE that the area of the circle = the area of the square + the area of the 4 rounded parts OUTSIDE the square.

The square has area 16.

How does the area of the 4 rounded parts OUTSIDE the square compare with the area of the square? Would the 4 pieces fit inside the square? I'd say that the 4 pieces would easily fit inside the square.
So, the total area of the 4 pieces is LESS THAN the area of the square.
In other words, the total area of the 4 pieces is LESS THAN 16.

So, the area of the circle = the area of the square + the area of the 4 rounded parts OUTSIDE the square.
= 16 + some value less than 16
= some value between 16 and 32

Now check the answer choices. To do so, let's say that pi is APPROXIMATELY 3

A) 2pi ≈ (2)(3) = 6
B) 4pi ≈ (4)(3) = 12
C) 8pi ≈ (8)(3) = 24
D) 12pi ≈ (12)(3) = 36
E) 16pi ≈ (16)(3) = 48

Notice that ONLY ONE answer choice is between 16 and 32.
So, the correct answer must be C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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