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2003 AMC 10A Problem 19

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2003 AMC 10A Problem 19AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 3 of 5 · about 4 min · position P16-20

A semicircle of diameter 11 sits at the top of a semicircle of diameter 22 , as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a lune. Determine the area of this lune.

figure

  1. A)

    16π−34\frac{1}{6}\pi-\frac{\sqrt{3}}{4}

  2. B)

    34−112π\frac{\sqrt{3}}{4}-\frac{1}{12}\pi

  3. C)

    34−124π\frac{\sqrt{3}}{4}-\frac{1}{24}\pi

  4. D)

    34+124π\frac{\sqrt{3}}{4}+\frac{1}{24}\pi

  5. E)

    34+112π\frac{\sqrt{3}}{4}+\frac{1}{12}\pi

Working