Surface and Volume

If you have studied geometry, you may remember that a cube with a volume of 1 cubic foot has a top surface area of 1 square foot. But if you double the volume of the cube, the top surface area is not doubled but is in fact only about 1½ times as large.

What in the world, you ask, does this have to do with cooking? Consider the following example.

Suppose you have a good recipe for ½ gal dessert sauce, which you normally make in a small saucepan. You want to make 16 gal sauce, so you multiply all ingredients by a conversion factor of 32 and make the sauce in a steam kettle. To your surprise, not only do you end up with more sauce than you expected, but it turns out rather thin and watery. What happened?