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03 Apr 2016, 03:06
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C
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:
88% (01:22) correct
12%
(01:29)
wrong
based on 100
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
circle.jpg [ 3.97 KiB | Viewed 6377 times ]
A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6
* A solution will be posted in two days.
03 Apr 2016, 03:33
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MathRevolution
Attachment:
circle.jpg
A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area?A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6
* A solution will be posted in two days.
Hi,
you will have to mention that the two circles meet at one point..
Area of larger circle =\(pi * r^2\)
for smaller circle, the diameter = r, so radius = r/2
Area of smaller circle = \(pi*(\frac{r}{2})^2\)
area of shaded region = \(pi * r^2\) - \(pi*(\frac{r}{2})^2\) = \(pi*(\frac{3}{4})*r^2\)
ratio= \((pi*(\frac{3}{4})*r^2)/(pi * r^2)\) = \(\frac{3}{4}\)
C
03 Apr 2016, 04:10
Kudos
Bookmarks
MathRevolution
Attachment:
The attachment circle.jpg is no longer available
A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area?A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6
* A solution will be posted in two days.
IMHO the best and easiest approach will be plugging in some values as below -
Attachment:
Circle 1.png [ 6.65 KiB | Viewed 6223 times ]
Area of the bigger circle will be π\((4)^2\) = 16π
Area of the smaller circle will be π\((2)^2\) = 4π
So, Area of the shaded region will be 16π - 4π = 12π
We are required to find -
Quote:
the ratio of the region shaded to the larger circle’s area?
The required ratio is 12π / 16π = 3/4
