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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:56) correct
35%
(02:04)
wrong
based on 37
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Not Attempted Yet
In the figure below, O1 and O2 are concentric circles and AB is tangent to O1 at C. If the radius of O1 is r and the radius of O2 is twice as long, what is the area of the shaded region?
A. \(\frac{\pi r^2}{2}\)
B. \(\pi r^2\)
C. \(\frac{3\pi r^2}{2}\)
D. \(2\pi r^2\)
E.\(3\pi r^2\)
Attachment:
2020-12-15_15-10-49.png [ 94.34 KiB | Viewed 2273 times ]
15 Dec 2020, 12:09
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Angle at the center= 60+60 = 120 degree
Area in grey= 2/3 * area of Large circle - 2/3 * area of small circle = 2/3 * pie (4r^2-r^2)= 2 Pie* r^2
So, I think, D.
Area in grey= 2/3 * area of Large circle - 2/3 * area of small circle = 2/3 * pie (4r^2-r^2)= 2 Pie* r^2
So, I think, D.
DinoPen
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02 Jan 2021, 20:03
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I wasn't actually sure how to get the correct numeric answer, but I did know that the Area of Outer circle - Area of Inner circle = 3 pi r^2.
If you half that (judging by the picture), the shaded area is larger than (3 pi r ^2 )/ 2
Thankfully, the image was 'drawn to scale'.
Thus, AC must be D.
TarunKumar1234
How do you know the angle is 60 degrees? Even if the sides are equivalent, the degrees don't have to match 60 degrees (thereby making it an equilateral) I might just be missing some triangle-circle property...
If you half that (judging by the picture), the shaded area is larger than (3 pi r ^2 )/ 2
Thankfully, the image was 'drawn to scale'.
Thus, AC must be D.
TarunKumar1234
How do you know the angle is 60 degrees? Even if the sides are equivalent, the degrees don't have to match 60 degrees (thereby making it an equilateral) I might just be missing some triangle-circle property...
