Double the area, Double the volume.
I was presented the following problem:
Using the classical tools (unmarked straightedge, marking device, and a compass [not the direction pointer]), consider a square with sides of 1 unit and an area of 1 square unit. Please construct a square that has double the area, 2 square units.
I figured out how to do that, no problem.
Then I was presented with the follow on.
Given a cube with the dimensions of 1x1x1 unit, "construct" a cube of double the volume. Again you are limited to the classical tools, assume that they can work in 3D space or that you can work on a sheet of paper that will be folded up into the cube.
I haven't given that one a solid go. Please keep the math simple and spoilerise.
