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In the figure above, a circular hole is cut in the center of a square

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In the figure above, a circular hole is cut in the center of a square [#permalink]

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New post 09 May 2017, 11:52
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In the figure above, a circular hole is cut in the center of a square sheet of metal. If the area of the sheet was 100 square centimeters before the hole was cut, what is the approximate area of the remainder of the sheet, in square centimeters, after the hole is cut?

A. 12.57
B. 49.73
C. 50.27
D. 71.73
E. 87.43
[Reveal] Spoiler: OA

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In the figure above, a circular hole is cut in the center of a square [#permalink]

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New post 09 May 2017, 12:06
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Consider the sides of the square to be A .

Then Area of the square is A^2 which is equal to 100 cm^2. Therefore A =10 cm (Since sides cannot be negative we cannot use -10).

If we draw a horizontal line passing through the center of the circle we get the value of the diameter of the circle ,

10 - (3+3) = 4 cm

Radius = Diameter/2 = 2 cm.

In order to get the area of the of the remaining metal sheet we subtract the area of circle from that of the square.

Area of the remaining metal sheet = A^2 - Pi*r^2 = 100 - Pi*(2^2)

100 - 3.14*(4) = 100 - 12.56.

The value that is closest to the following value is option E. Hence Option E is the Answer.
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Last edited by Kritesh on 21 May 2017, 02:39, edited 1 time in total.
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Re: In the figure above, a circular hole is cut in the center of a square [#permalink]

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New post 09 May 2017, 12:07
Since the area of the paper is 100sq cm, the side of the square is 10cm.

From that we can deduce the diameter of the circle to be 10-6(4 cm). Hence, area of the circle is pi*2^2 or 88/7

Area of remainder of sheet after the hole is cut is
100 - 88/7
= 612/7
= 87.43(Option E)

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In the figure above, a circular hole is cut in the center of a square [#permalink]

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Area of square= 100 sq cm
Therefore, Side of Square= 10 cm

From the given diagram
Diameter of Circle= 10-6=4 cm
Radius of Circle= \(\frac{4}{2}\)= 2
Area of Circle= \(\pi\)\(r^2\)
=\(\frac{22}{7}\)*2*2= \(\frac{88}{7}\)

Area of the remaining sheet= 100-\(\frac{88}{7}\)= 100- 12.5= 87.5

Answer: E.

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In the figure above, a circular hole is cut in the center of a square [#permalink]

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New post 12 May 2017, 12:41
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SajjadAhmad wrote:
In the figure above, a circular hole is cut in the center of a square sheet of metal. If the area of the sheet was 100 square centimeters before the hole was cut, what is the approximate area of the remainder of the sheet, in square centimeters, after the hole is cut?

A. 12.57
B. 49.73
C. 50.27
D. 71.73
E. 87.43


We are given that the area of the sheet is 100 cm^2. Since area = side^2, the side of of the sheet is equal to 10.

In referencing the given diagram we see that the diameter of the circle must equal 10 - 3 - 3 = 4 cm, and thus the radius is 2 cm. Let’s now determine the area of the circle.

area = π(radius)^2

area = π(2)^2 = 4π = 4 x 3.14 = 12.56 cm^2

Thus, the area of the remainder of the sheet is 100 - 12.56 = 87.44, which is about 87.43.

Answer: E
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In the figure above, a circular hole is cut in the center of a square   [#permalink] 12 May 2017, 12:41
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