AMC 10 Step by Step
Log inSign up
Printable

2015 AMC 10B Problem 9

Include the solutionBack to the problem
2015 AMC 10B Problem 9AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 2 of 5 · about 2 min · position P1-10

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 33 and center (0,0)(0,0) that lies in the first quadrant, the portion of the circle with radius 32\tfrac{3}{2} and center (0,32)(0,\tfrac{3}{2}) that lies in the first quadrant, and the line segment from (0,0)(0,0) to (3,0)(3,0) . What is the area of the shark's fin falcata?

figure

  1. A)

    4π5\dfrac{4\pi}{5}

  2. B)

    9π8\dfrac{9\pi}{8}

  3. C)

    4π3\dfrac{4\pi}{3}

  4. D)

    7π5\dfrac{7\pi}{5}

  5. E)

    3π2\dfrac{3\pi}{2}

Working