Bat Caves

(A true story) Two mammalogists were capturing bats that originated from one of two caves. The caves were located 500 meters apart. If the bats forage in a circular region that has a center at the cave and that has a radius of 3 kilometers, what is the area of the overlap of the forgaging area of the two caves?

Use graph paper and a compass to graph the regions for the two caves and use this to estimate or compute the area of the overlapping region.

Explain your method of estimating the area.

How does the size of the area of the overlapping region compare to the size of the area of one of the circles?