【正确答案】 B

【答案解析】The area of the shaded region is the area of quarter-circle AOB minus the area of the square. Since r = OA = 6, the area of the quarter-circle is[*] OY, the diagonal of the square, is 6 (since it is a radius of the circle), so OZ, the side of the square, is[*] [See KEY FACT J8]. So the area of the square is[*] Finally, the area of the shaded region is 9π- 18, which is approximately 10. **The solution above requires several steps. [See Sections 11-J, K, L to review any of the facts used.] If you can't reason through this, you still should be able to answer this question correctly. Use TACTIC 6. The shaded region has a definite area, which is either 12, more than 12, or less than 12. Eliminate D. Also, the area of a curved region almost always involves π, so assume the area isn't exactly 12. Himinate Choice C. You can now guess between Choices A and B, but if you trust the diagram and know a little bit you can improve your guess. If you know that the area of the circle is 36π, so that the quarter-circle is 9π or about 28, you can estimate the shaded region. It's well less than half of the quarter-circle, so less than 14 and probably less than 12. Guess Choice B.