Circle with square cross sections

[nomathwiz]

Homework Statement

The base of S is a circular disk with radius 2r. Parallel cross-sections perpendicular to the base are squares.
Find the volume V of this solid.

Homework Equations

The Attempt at a Solution

I'm clueless

 

[Mark44]

Draw a sketch of the 3D solid in this way.
Draw a circle of radius 2r (so diameter is 4r), with its center at (0, 0).
Draw several line segments across the circle, and parallel to the x-axis from one side to another. For each of these line segments, draw a square whose height is equal to its width. If you think about it, the maximum square will be on the x-axis, and the sizes of the squares taper off as you go up or down the y-axis.
Does that help?