Expert: Josh - 1/26/2010

Question
Lake Mead is an artificial lake formed by the hoover dam, covering parts of both Arizona and Nevada. It has a surface area of 640 km squared. The area has been experiencing a drought since 2005, and the water level has dropped 16.8 meters. How many cubic kilometers of water have disappeared during this drought?

The general approach of this question confuses me, Once I see what I need to convert and the correct order I would better understand it.

Answer
Okay Mike. In the word "kilometer", think of "kilo-" as a prefix. All it does is basically multiplies the unit ("meter") by a 1000.

So, 1 [kilometer] = 1000 [meter]. If we divide both sides by 1000, we get
   1/1000 [kilometer] = 1 [meter]. For convenience, I'll swap the LHS with the RHS and write this as
   1 [meter] = 1/1000 or 0.001 [kilometer]   ....[#1]

The dam is shaped like a cylinder. Its area remains constant at 640 [km^2] (square kilometer) irrespective of its height. So, its volume equals area times height.

V [km^3] (cubic kilometer) = A [km^2] * H [km]  ....[#2]

The key is to be consistent and use compatible units of measurement on both sides of the equation. Here, I have taken the liberty to express the height (originally in meters) in terms of kilometer.

Using the conversion in [#1],
height H = 16.8 [meter] * 1[kilometer]/1000[meter] = 0.0168 [kilometer]

Knowing A = 640 [km^2], plugging H = 0.0168 [km] into equation [#2] tells you how much water has disappeared, in cubic kilometer [km^3]. It involves only one multiplication V=A*H.