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2015 AMC 10B Question 9

AMC10 · 2015 AMC 10B

Question 9

The shaded region below is called a shark’s fin falcata, a figure studied by Leonardo da Vinci. It is bounded by the portion of the circle of radius $3$ and center $(0,0)$ that lies in the first quadrant, the portion of the circle with radius $\tfrac{3}{2}$ and center $(0,\tfrac{3}{2})$ that lies in the first quadrant, and the line segment from $(0,0)$ to $(3,0).$ What is the area of the shark’s fin falcata?

Question illustration
  1. $ \dfrac{4\pi}{5} $
  2. $ \dfrac{9\pi}{8} $
  3. $ \dfrac{4\pi}{3} $
  4. $ \dfrac{7\pi}{5} $
  5. $ \dfrac{3\pi}{2} $