__Category__: Solid Geometry"Published in Vacaville, California, USA"

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

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

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

or