In the diagram, the three concentric circles have radii of 4, 6, and 7. Three regions are labeled X, Y, or Z below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form.
+9479 So all you are doing is the area of circle Z minus the area of circle X.
The area of a circle is pi times the radius squared.
Circle Z has a radius of 7.
Circle X has a radius of 4.
So
the area of circle Z = (pi)(72) = 49pi , and
the area of circle X = (pi)(42) = 16pi .
49pi - 16pi = 33pi
