If a = 6l^2 is the total area of the surface of a cube with sides l length and A = 6 (2l)^2 is that area with 2l sides, then we take the ratio A/a = 6 (2l)^2/(6 l^2) = (2l)^2/l^2 = 4l^2/l^2 = 4. So that A = 4a. And that explicitly shows that the area A with 2l for sides is 4 X a, where a is the area when l is the side length.
<span>Using ratios to compare values of the same thing is the smart way to solve this kind of problem, because many of the values, like the 6 in both, cancel out. In fact, because we found that A/a = (2l/l)^2 we say in general that the area of a cube varies with the square of the length of its side.
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