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Find the volume of the largest cylinder with circular base that can be inscribed in a cube whose volume is 27 cu. in.
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 |
In this problem, the volume of a cube is given. The length of the edge of a cube is
If the circular arc of the base of a cylinder is tangent to the bottom edges of a cube, then it follows that
where x is the length of the edge of a cube and r is the radius of a circle. The radius of a circle is
Therefore, the volume of the largest cylinder that can be inscribed in a cube is
But
Hence, the above equation becomes,
