MathDB

2

Part of 1985 AMC 12/AHSME

Problems(1)

Shape of a Monster

Source:

3/2/2009
In an arcade game, the "monster" is the shaded sector of a circle of radius 1 1 cm, as shown in the figure. The missing piece (the mouth) has central angle 60∘ 60^{\circ}. What is the perimeter of the monster in cm?
[asy]size(100); defaultpen(linewidth(0.7)); filldraw(Arc(origin,1,30,330)--dir(330)--origin--dir(30)--cycle, yellow, black); label("1", (sqrt(3)/4, 1/4), NW); label("60∘60^\circ", (1,0)); [/asy]
(A)\ \pi \plus{} 2 \qquad (B)\ 2\pi \qquad (C)\ \frac53 \pi \qquad (D)\ \frac56 \pi \plus{} 2 \qquad (E)\ \frac53 \pi \plus{} 2
geometryperimeter