MathRevolution wrote:
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.
From Figure we see that
radius of bigger circle = Diameter of smaller circle
Let, Radius of Bigger circle = 2 = Diameter of smaller circle
i.e. Radius of Smaller circle = 2/2 = 1
Area of Bigger circle = Pi 2^2 = 4 Pi
Area of Smaller circle = Pi 1^2 = Pi
Area of Shaded Region = Big circle - Small Circle = 4 Pi - Pi = 3Pi
Shaded Area/Area of Big circle = 3Pi/4 Pi = 3/4
Answer: Option C
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