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1985 AMC 12 Question 2

AMC12 · 1985 AMC 12

Question 2

In an arcade game, the “monster” is the shaded sector of a circle of radius $1$ cm, as shown in the figure. The missing piece (the mouth) has central angle $60^\circ.$ What is the perimeter of the monster in cm?

Question illustration
  1. $\pi+2$
  2. $2\pi$
  3. $\frac53\pi$
  4. $\frac56\pi+2$
  5. $\frac53\pi+2$