SOLUTION: The base of a regular square pyramid is inscribed in the base of a cylinder. The height of the cylinder is triple the height of the pyramid. Find the ratio of the volume of the p

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The base of a regular square pyramid is inscribed in the base of a cylinder. The height of the cylinder is triple the height of the pyramid. Find the ratio of the volume of the p      Log On

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Question 74597: The base of a regular square pyramid is inscribed in the base of a cylinder. The height of the cylinder is triple the height of the pyramid. Find the ratio of the volume of the pyramid to the volume of the cylinder.

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
For a square inscribed in a circle, the diagonal of the square is twice the radius of the circle.

area of circle is pi%2Ar%5E2

area of square is 2r%5E2

the volume of a pyramid is %28%28area-of-base%29%2A%28height%29%29%2F3 in this case%282r%5E2h%29%2F3

the volume of a cylinder is %28area-of-base%29%2A%28height%29 in this case pi%2Ar%5E2%2A3h

the ratio of the volumes is %28%282r%5E2h%29%2F3%29%2F%28pi%2Ar%5E2%2A3h%29

multiplying the top and bottom of the fraction by 3 and cancelling the h and the r%5E2 leaves 2%2F%289pi%29