PAC-MAN is a circle of radius 24 with a sector of angle π/3 removed. PAC-MAN eats circular pellets of radius 2. If PAC-MAN wants to eat pellets that have that same total area that he does, how many pellets must he eat?

Answer 1

area of PAC-MAN = (5/18) (π(24)^2)
=160π

area of 1 pellet = 4π

number of pellets equal to PAC-MAN = 160π/(4π) = 40

Answer 2

The area of a circle of radius 24 is 576π. The missing sector is 16 of the circle, so the area of PAC-MAN is 480π. A circular pellet of radius 2 has area 4π, so the number that PAC-MAN needs to eat is 480π4π=120.