AMC 8 Daily Practice - Circles

Complete problem set with solutions and individual problem pages

Problem 8 Easy

With each of the three vertices of an equilateral triangle with a side length of 2 centimeters as the center, arcs are drawn with a radius of 2 centimeters. What is the perimeter of the shaded figure in centimeters? (Take \pi = 3.14)

  • A.

    3.14

  • B.

    6.28

  • C.

    9.42

  • D.

    12.56

  • E.

    15.7

Answer:D

Each arc is \frac{1}{6} of the circumference of a circle because the central angle of each arc is 60^\circ.

Therefore, the perimeter of the shaded figure is composed of 6 such arcs.

The length of one arc is: \frac{1}{6} \times 2\pi r = \frac{1}{6} \times 2 \times 3.14 \times 2

The total perimeter of the shaded figure is: 6 \times \left( \frac{1}{6} \times 2 \times 3.14 \times 2 \right) = 2 \times 3.14 \times 2 = 12.56 \text{ centimeters}

Thus, the perimeter of the shaded figure is \boxed{12.56} centimeters.

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