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Old 2006-06-29, 05:26   #1
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Aug 2003
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Default Double the area, Double the volume.

I was presented the following problem:
Using the classical tools (unmarked straight-edge, 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.
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