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A cylinder whose base is a circle is circumscribed about a right prism of altitude 12.6 ft. Find the volume of the cylinder if the base of the prism is a square of edge 3 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 |
Consider the base of a cylinder which is a circle that circumscribed about a square as follows
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| Photo by Math Principles in Everyday Life |
The length of the diagonal of a square is equal to the diameter of a circle. By Pythagorean Theorem, the diameter of a circle is
Therefore, the volume of a circular cylinder is
But
Hence, the above equation becomes
