Another way to think about it: It's because 1.5 > √2.<p>To exactly double the area of a figure, scale any linear dimension up by √2. If you scale by more than that, you'll more than double the area.
For area, the change in size is the square of the old:new ratio.<p>Two dimensions, so X * X<p>For volume, the change in size is the cube of the old:new ratio.<p>Three dimensions, so X * X * X