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23 Feb 2012, 01:53
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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:
45%
(medium)
Question Stats:
64% (01:26) correct
36%
(01:49)
wrong
based on 61
sessions
History
Date
Time
Result
Not Attempted Yet
A circle is inscribed in a half circle with a diameter of \(\pi\) . What is the ratio of the area of the half circle to the area not covered by the inscribed circle?
1:1
1:2
1:4
3:4
2:1
I know this has been discussed before & answer is easy to figure out. But my doubt is how to figure out the area of the inscribed circle.
1:1
1:2
1:4
3:4
2:1
I know this has been discussed before & answer is easy to figure out. But my doubt is how to figure out the area of the inscribed circle.
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23 Feb 2012, 03:46
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GMATPASSION
This question needs a revision, because there are infinitely many circles possible to inscribe in a semicircle. Consider just two cases below:
Attachment:
Semicircle.PNG [ 18.1 KiB | Viewed 21946 times ]
Anyway, for that case we don't really need any formula to get the ratio:
Since the radius of the big circle (\(\frac{\pi}{2}\)) is twice the radius of the inscribed circle (\(\frac{\pi}{4}\)) then its area is 4 times greater then the area of the inscribed circle (because in the area formula the radius is squared. For example the area of a circle with radius of 2 is \(4\pi\), which is 4 times greater than the radius of a circle with the radius of 1, which is \(\pi\)).
Thus the are of the semicircle is 4/2=2 times greater than the area of the inscribed circle: the area of the semicircle 2 units, the area of the inscribed circle 1 unit, and the area of the semicircle not covered by the inscribed circle is also 1. Ratio: 2/1.
Answer: E.
Hope it's clear.
23 Feb 2012, 04:12
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E is the answer.
The inscribed circle will have diameter equal to radius of half circle....
area of unshaded region would be = area of semi-circle - area of inscribed circle
The inscribed circle will have diameter equal to radius of half circle....
area of unshaded region would be = area of semi-circle - area of inscribed circle
