This problem is a very important problem, IMHO, and teaches many important lessons... and not just in math.
At first, this problem seems very complicated with the height and the mass and stuff that's per cubic centimeter and all. It seems like a very complicated, complex problem.
However, as several people here have well-demonstrated, it's really two problems that have been intertwined. Once you separate the two smaller problems, neither is very difficult.
A lot of "higher" math is this way. It's just a lot of simple problems that have been intertwined. Here's an interesting fact: if you can add, subtract, multiply, and divide, then you can do all math operations because all higher operations are definded based on those four simple operations. And when you consider the fact that muliplying is just repeated adding and dividing is just repeated subtracting, well you see that from about third grade on, math is just increasing intertwining and even the most seemingly-complex problem breaks down into simple operations.
Life is often like this too. Seemingly huge, complex problems break down into just a series of little problems that are intertwined. Huge tasks break down into just a series of simple tasks.
It's important to learn that when you face a big problem -- be it a math problem or a marriage problem -- don't be intimidated by the seeming complexity or enormity of it. Just break it down into little pieces.
The other thing this problem teaches is an approach to problem solving. The first step in my previous assertions is to separate the intertwined problems. The approach to learn is to write down what you know and start filling in the blanks. This is how a detective often solves a mystery. It's how many problems in life in general can be approached. Just start writing down what you know and see how the pieces fit together.
:foot:
