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Math Expert V
Joined: 02 Sep 2009
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If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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Difficulty:   5% (low)

Question Stats: 82% (00:50) correct 18% (01:11) wrong based on 120 sessions

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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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Attachment: 2014-11-24_1823.png [ 3.4 KiB | Viewed 2261 times ]

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GMAT 1: 700 Q47 V39 Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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If the length of the side of the square is 4 units, the radius of the circle must be 2 units. Therefore, the area of the circle is πr^2 = π(4) = 3.1415 * 4 = approx. 13 units.

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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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Side of the square is $$4$$ units.
Diameter of circle = side of square =$$4$$
Radius(r) of circle = $$\frac{Diameter}{2}$$ =$$\frac{4}{2}$$ =2
Area of circle = pi$$r^2$$ --PS: i don't know how to insert π notation so i used pi.--

Area of circle= $$3.14*2^2$$ $$=12.56$$
Area is approx $$13$$ unit

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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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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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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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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.

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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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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)

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Math Expert V
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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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Bunuel wrote:
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

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.

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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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Bunuel wrote:
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.

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Re: If the figure below is a square with a side of 4 units, what is the ar  [#permalink]

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Bunuel wrote:
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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How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Re: If the figure below is a square with a side of 4 units, what is the ar   [#permalink] 23 Jan 2018, 10:19
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