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Find the volume of the largest right circular cylinder that can be circumscribed about a rectangular parallelepiped of dimensions 2 ft. by 3 ft. by 4 ft.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
There are three ways in finding the volume of a right circular cylinder that circumscribed about a rectangular parallelepiped but we have to choose the largest volume.
If a = 2 ft., b = 3 ft., and c = 4 ft., then the volume of a right circular cylinder is
If a = 3 ft., b = 2 ft., and c = 4 ft., then the volume of a right circular cylinder is
If a = 2 ft., b = 4 ft., and c = 3 ft., then the volume of a right circular cylinder is
Therefore, the volume of the largest right circular cylinder that can be circumscribed about a rectangular parallelepiped is
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