+1248 A rectangle with vertices A(0,0), B(5,0), C(5,3) and D(0,3) is graphed in a coordinate plane. The rectangular region determined by those points is rotated $360^\circ$ about the line $y=-2$, forming a geometric solid. The rectangular region is then rotated $360^\circ$ about the $x=-5$, forming another geometric solid. How many cubic units are in the positive difference between the volumes of those two geometric solids? Express your answer in terms of $\pi$.
+129771 Volumes =
Volume of outside cylinder - Volume of inside cylinder
First solid volume
pi (3 - -2)^2 * 5 - pi(0 - - 2)^2 * 5 =
pi [ 125 - 20] =
105 pi
Second solid volume
pi (5 - -5)^2 * 3 - pi (0 - -5)^2 * 3 =
pi [ 300 - 75] =
225 pi
Difference in volumes = (225 - 105 ) pi = 120 pi
