Shape of a Monster
Source:
March 2, 2009
geometryperimeter
Problem Statement
In an arcade game, the "monster" is the shaded sector of a circle of radius cm, as shown in the figure. The missing piece (the mouth) has central angle . 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("", (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