A general rule for this that I learned from my geometry teacher was that if you have a cube and you find the diagonal that cuts through the center of it, the answer would be the length of a side times the square root of 3. So for this question, it would be 3 x square root 3.
Another way, I guess which explains it using the Pythagorean theorem, would be, if you found the length of a diagonal on a surface of the cube (which would be 3 x square root 2) and then found the diagonal through the center of the cube by creating a right triangle connecting with an edge of the cube, the diagonal drawn on one square of the cube, and the diagonal cutting through the center of the cube. In this case, it would be that c^2=a^2+b^2 where a is one edge of the cube and b is the diagonal on a side of the cube. therefore, c^2=3^2+(3^2 x 2) which equals 3 x 3^2 (because you now have 3 3^2s) and if you take the square root of it all to find c, you end up with 3 x square root 3.
Another way, I guess which explains it using the Pythagorean theorem, would be, if you found the length of a diagonal on a surface of the cube (which would be 3 x square root 2) and then found the diagonal through the center of the cube by creating a right triangle connecting with an edge of the cube, the diagonal drawn on one square of the cube, and the diagonal cutting through the center of the cube. In this case, it would be that c^2=a^2+b^2 where a is one edge of the cube and b is the diagonal on a side of the cube. therefore, c^2=3^2+(3^2 x 2) which equals 3 x 3^2 (because you now have 3 3^2s) and if you take the square root of it all to find c, you end up with 3 x square root 3.
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3(sqrt(3))