Hello, Karen,
I'm assuming the question is asking what characteristics of a written value allow us to distinguish between area and volume. The units provide the evisence.
Numbers describing area should have units such as ft2, cm2, km2, acres, or any number of other units that are the result of two lengths multiplied together. Units of area are two-dimensional (in a 3 dimensional space).
Units of volume will have units such cm3, liters. m3, gallons, ml, and many ohers.
Units not only communicate the meaning of a value, they are also important in guiding math calculations. You'll hear "keep the units" while doing calculations. While this can slow down the calculation, waste good pencil lead, and be frustratng, it also helps prevent mistakes. If you keep the units throughout and cancel the ones you can, the ending unit should match what would be expected. If you are calculating a volume and wind up with kg/m2, something is wrong in the calculation. Basic operations, such as converting moles HCl to grams HCl is easy when you keep the units. Which is correct: do we multiply or divide the two numbers:
Given 10 grams/mole and 5 moles, and we want grams. It is easy to see:
(5 moles)(10 grams/mole) = 50 grams
Going the other way (how many moles are in 50 grams) isn't as obvious, until units are used:
(50 grams)/(10 grams/mole) = 5 moles
Units are important for communication: The 1998 NASA launch of a $125 million space probe to Mars, to study it's weather, ended in failure when the probe's thrusters did not slow the vehicle for entry into Mars' atmosphere. Engineers at the Jet Propulsion Laboratory (JPL) used the metric system of millimeters and meters in its calculations, while Lockheed Martin Astronautics in Denver, Colorado, which designed and built the spacecraft, provided crucial acceleration data in the English system of inches, feet, and pounds. As a result, the craft did not produce the correct thrust when decelerating, and presumably burned up on entry.
Sorry - Long response to a straightforward question. But I was one of those who resisted keeping units in my calculations. I did OK, a few mistakes, but, overall, still not worth the hassle for a few points. Then, during a physics lecture for 20+ students, I drew a blank on the next step in a physics calculation dealing with force and torque. But I had had kept the units and saw that a division of a value of length was required for the unit to become the metruic unit for a Newton, the SI unit of force, and the expected outcome of the calculation. It became obvious what was needed for the last step of the calculation. (Don't tell my class I was lost).
Bob