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Math Help - Volume between two shapes (one inscribed in the other)

  1. #1
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    Volume between two shapes (one inscribed in the other)

    Problem: If a square prism is inscribed in a right circular cylinder of radius 3 and height 6, the volume inside the cylinder but outside the prism is?

    I know I need to subtract the volume of the square prism from the cylinder. The volume of the cylinder is 54pi. I am having trouble visualizing/drawing a diagram to get the side length of the square.

    The answer is 61.6, and the side length of the square is 3 times the square root of 2. Thanks!
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  2. #2
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    Re: Volume between two shapes (one inscribed in the other)

    Did you draw a circle with a square in it? The radius of the circle is 3 and half the diagonal of the square is the same thing. What is the length of the side of the square in this cross-sectional drawing? Hint: 45-45-90.
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