A lump of solid material was found
to weigh 22.5 grams. When placed in 100 centimeters
cubed of water, the volume increased by three centimeters cubed. What is the density of the lump of
For this question, we need to
calculate the density of the lump of solid material. Although this problem focuses on
density, let us first discuss matter so we can understand this term better.
Matter is everything around us that
is made up of particles, such as the solid material in this example. Matter must have mass and occupy
space. Since matter has mass and must
occupy space, it must also have density. The density of a substance is
expressed as mass per unit volume. The reason matter must have density
is because both matter and density have mass associated with it, as well as volume,
which is nothing more than the space a substance occupies.
When looking at the description of
density, we should note that the word “per” means a ratio or fraction can be created
for density. Density can be expressed as an
equation where it is equal to mass divided by volume.
Let us take a look back at our
problem to see if we can identify the mass and volume. The problem states that the solid
material is 22.5 grams, which is the mass. There are two volumes in our
problem: 100 centimeters cubed and three centimeters cubed. The 100 centimeters cubed is the
volume of water before the solid material was placed in the graduated cylinder. So we should not include this
volume since the problem is asking us to find the density of the solid material.
The problem also states the volume
increased by three centimeters cubed after the lump of solid was added to the
graduated cylinder. So the volume of the solid material
is three centimeters cubed. Now we can use our density
equation. We can substitute 22.5 grams in for
the mass and three centimeters cubed as the volume into our equation. Then we divide 22.5 grams by three
centimeters cubed to calculate a density of 7.5 grams per centimeters cubed.
Notice how the units for mass and
volume do not cancel out since they are not the same. This is why the unit for density is
expressed as grams per centimeters cubed. Therefore, the density of the lump
of solid material is 7.5 grams per centimeters cubed.