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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 an equilateral triangle of side 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 |
Consider the base of a cylinder which is a circle that circumscribed about an equilateral triangle as follows
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| Photo by Math Principles in Everyday Life |
The radius of a circle is equal to two thirds of the altitude of an equilateral triangle. By Pythagorean Theorem, the altitude of an equilateral triangle is
Hence, the radius of a circle is
Therefore, the volume of a circular cylinder is
But
Hence, the above equation becomes
