SAT Math Multiple Choice Practice Question 113: Answer and Explanation

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Question: 113


If the diameter of circle O is 10 cm, and ABCD is a square, then the area of the shaded region in cm2 is which of the following?

A. 25π - 50
B. 25π - 25
C. 50π - 50
D. 50π - 100
E. 100π - 100

Correct Answer: A


A. Because the circle's diameter is 10, its radius is 5, and its area is πr2 = 25π. The square's diagonal cuts it into two 45-45-90 triangles, so just like in Question 7, one side of the square must measure , and its area must be . The shaded area just equals the circle's area minus the square's.

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