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09 May 2017, 12:52
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
89% (01:40) correct
11%
(01:49)
wrong
based on 56
sessions
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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
A. 12.57
B. 49.73
C. 50.27
D. 71.73
E. 87.43
Attachments
Untitled.jpg [ 16.06 KiB | Viewed 3228 times ]
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.
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.
09 May 2017, 13:07
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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)
Sent from my LG-H818 using GMAT Club Forum mobile app
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)
Sent from my LG-H818 using GMAT Club Forum mobile app
