### Video Transcript

Which of the following statements
best defines the density of a substance? (A) The weight per unit mass of a
substance. (B) The area per unit volume of a
substance. (C) The hardness per unit volume of
a substance. (D) The mass per unit volume of a
substance. (E) The thickness per unit area of
a substance.

The question mentions the word
“density.” We are asked to select the
statement which best defines this word. So, what is density? Density is a value given to a
substance when we take its mass and divide it by its volume. So, let’s say we have a solid
substance, for example, a piece of aluminum. We can measure its mass using a
scale or balance. We can measure the mass of a
substance in grams, whose symbol is lowercase g. Then, we can measure the volume of
the substance.

We know that we can calculate the
volume of a cube or a rectangular cuboid using the formula volume equals length
times width times height, like this. If each side is measured using the
unit centimeters, then we get centimeters times centimeters times centimeters. This gives us an answer whose unit
is centimeters cubed.

So usually, we measure volume in
centimeters cubed, whose unit is cm to the power of three. Of course, not all substances have
a nice cubic or rectangular cuboid shape. Some substances and objects have an
odd, or irregular, shape like a stone or an iron nail, for example. If we want to determine the density
of such objects, we can first easily measure their mass on a scale or balance. However, we cannot use the formula
volume equals length times width times height to determine the volume.

So how do we determine the
volume? In this case, we can place the
substance or object into water in a measuring apparatus called a measuring
cylinder. We will notice the water level rise
above its initial or starting level. We call this water
displacement. The new water level after the stone
is added will be higher than the starting water level before the stone was
added. The height by which the water level
rises when the object is placed into the water tells us the volume of that
object. In other words, the difference
between the water starting level and its final level tells us the volume of the
stone. So this is how we determine the
volume of the stone.

Now, don’t be confused. The measuring cylinder uses
milliliters for volume, but we want centimeters cubed. It turns out that a milliliter is
the same volume as a centimeter cubed. So any value we have in milliliters
is the same value in centimeters cubed. So, we can determine the mass and
volume of solid substances or objects. And we can use similar methods to
measure the mass and volume of gases and liquids too.

Now that we know how to determine
the mass and volume of a substance, what then is density? We said density is a value given to
a substance when we take its mass and divide this value by its volume. Taking grams and dividing by
centimeters cubed, we get a unit for density of grams per centimeter cubed, which we
write as g forward slash cm three. So, another way to define density
is, it is the mass per unit volume of a substance. We can see this definition matches
answer choice (D).

The statement which best defines
the density of a substance is (D): the mass per unit volume of a substance.