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Answer = D) 13

Circle is inscribed, so radius = 2

\(Area = \pi 2^2 = 3.14 * 4 = 12.56 \approx{13}\)
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From the figure the diameter of the circle =4 units

So area = Area = 3.15*r^2=3.15*4 =13 Approx.


Answer D
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Diameter of the circle = Side of the square = 4 units

Area of the circle = 3.14 * (Diameter)^2/4 = 3.14* 16/4 = 12.56 = 13 (Approx)

Answer D.
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Bunuel
If the figure below is a square with a side of 4 units, what is the area of the enclosed circle, expressed to the nearest whole number?

A) π
B) 4
C) 8
D) 13
E) 16

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Source: Chili Hot GMAT

Official Solution:

If the figure below is a square with a side of 4 units, what is the area of the enclosed circle, expressed to the nearest whole number?


A) π
B) 4
C) 8
D) 13
E) 16

Eyeballing:
Eyeballing is a parallel technique to be used on diagrams. Note that whatever the area of this circle may be, it must be less than the area of this square. The area of the square (in square units) is: A = s^2 = 4 × 4 = 16. Therefore, the area of the circle is a little less than 16. Choice D is the only close answer. For the record, the near exact area of the circle is: A = π^2 = 3.14(2)^2 = 12.56 or 13. Note that the decimal approximation for π is 3.14 while the fractional approximation is 22/7.

Answer: D.
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Bunuel
If the figure below is a square with a side of 4 units, what is the area of the enclosed circle, expressed to the nearest whole number?
Attachment:
2014-11-24_1823.png

A) π
B) 4
C) 8
D) 13
E) 16

Since the square has a side of 4, the diameter of the circle is 4, and the radius is 2.

Thus, the area is π x 2^2 = 4π ≈ 4 x 3.14 = 12.56. The nearest integer to 12.56 is 13.

Answer: D
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Bunuel
If the figure below is a square with a side of 4 units, what is the area of the enclosed circle, expressed to the nearest whole number?


A) π
B) 4
C) 8
D) 13
E) 16

Kudos for a correct solution.

Source: Chili Hot GMAT

Attachment:
2014-11-24_1823.png

Radius of the circle is 2 units.

Area of the circle is \(π2^2\) = \(4π\) ~ \(13\) , Answer will be (D)
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