The density, d, of an object is given by the following formula, where m represents the mass of the object and V represents the volume of the object.
Heather was asked to find the density of a brick given the mass in kilograms and the dimensions of the brick in meters. She wrote her answer, 2,400 kilograms per square meter, on the chalkboard. Without even performing the calculations first, Jonathan knew right away that her answer was incorrect. How could he tell there was an error?
The units should be kilograms per cubic meter.
The units should be kilograms per meter.
The units should be kilograms.
The units should be cubic meters.
The units should be kilograms per cubic meter.
The units should be kilograms per cubic meter. You see, Jonathan has a keen eye for detail and he knows that density is measured in terms of mass per unit volume. In this case, the units should be kilograms per cubic meter, not kilograms per square meter. A square meter is a measure of area, but density is a measure of mass divided by volume. So Jonathan knew right away that Heather made an error in her answer. Lucky for her, Jonathan was there to save the day!
The correct answer is "The units should be kilograms per cubic meter."
Jonathan could tell there was an error because the density, d, is a measure of mass per unit volume. Therefore, the units of density should be in kilograms per cubic meter (kg/m³), not kilograms per square meter (kg/m²) or kilograms per meter (kg/m) as stated by Heather in her answer. The correct units for density take into account the three-dimensional nature of the object's volume, not just its length or surface area.