SAT Math Multiple Choice Practice Question 125: Answer and Explanation

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Question: 125


In the diagram above, O is the center of the large circle, and A and B are the centers of the two smaller circles. If the length of NP is 8, then the area of the shaded region is

A. 4π
B. 8π
C. 16π
D. 32π
E. 48π

Correct Answer: B


B. Because the whole circle has a diameter of 8, its radius is 4 and its area is πr2, or 16π. (Don't fall into the common trap of squaring the diameter by accident.) Each smaller circle has half the radius of the large one, which is 2, so each one has an area of 4π. There you go: The shaded area is 16π - (2 × 4π) = 16π - 8π = 8π.

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