SAT I 一日一问：2013年3月15日-打印版式-

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

In the figure above, a shaded circle with diameter line C D is tangent to a large semicircle with diameter line A B at points and . Point is the center of the semicircle, and is perpendicular to . If the area of the large semicircle is , what is the area of the shaded circle?

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The Correct answer is C.

Explanation

Segment line C D is a radius of the large semicircle, and it is also a diameter of the shaded circle, so the radius of the large semicircle is equal to twice the radius of the shaded circle. Let be the radius of the shaded circle. Then 2 times r is the radius of the large semicircle, and so the area of the semicircle is (pi times (2 times r)^2) over 2 = (4 times pi times r^2) over 2 = 2 times pi times r^2 . This area is given as , and so the area of the shaded circle is (pi times r^2) = (2 times pi times r^2) over 2 = 24 over 2 = 12 .