Thread: 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!

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.