How can each pool be considered "deepest"?

Question

Suppose there are 2 rectangular pools: One is 30 feet wide, 60 feet long, and 5 feet deep throughout, and the other is 40 feet wide, 50 feet long, and 4 feet deep throughout. Show that each pool can be considered "biggest" by comparing the sizes of the pools in two meaningful ways other than by comparing one-dimensional aspects of the pools. 

Answer 1

The surface area and volume of the first pool are:

• Area = 30 ft * 60 ft = 1800 ft²
• Volume = 1800 ft²*5 ft = 9000 ft³

 

The surface area and volume of the second pool are:

• Area = 50 ft * 50 ft = 2000 ft²
• Volume = 2000 ft² * 4 ft = 8000 ft³

 

So the second pool has a larger surface area, so it would appear larger on a map.  But the first pool has a larger volume, so it holds more water.