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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 $\pi$.

 Jan 14, 2024
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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

 

 

cool cool cool

 Jan 14, 2024

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