The mass of a sample of material can easily be calculated if we are given the
density and the volume.
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
In this example, we’re given that iron has a density of 7.8 grams per cubic centimeter,
and we’re asked to find the mass of a 35 cubic centimeter sample of iron.
volume × density =
mass
× volume
volume
The
density
formula
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
In all problems having to do with density, we can start with the density formula,
density equals mass divided by volume.
volume × density =
mass
× volume
volume
The
density
formula
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
In this problem, we’re asked for the mass and we’re given the density and the
volume.
volume × density =
mass
× volume
volume
Solve this
Equation for
Mass
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
So we need to rearrange this equation to solve for mass. In other words we need to
get the word mass on one side of the equation, all by itself.
volume × density =
mass
× volume
volume
We need to cancel out
volume from here
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
To get mass by itself on the right side of the equation, we need to cancel out
volume from the denominator here
volume × density =
mass
× volume
volume
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
We can do something to an equation as long as we do the same thing to both sides,
so we’ll multiply both sides of the equation by volume (click) like this
volume × density =
mass
× volume
volume
These can be
cancelled
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
On the right side we have volume both in the numerator and the denominator, so
we can (click) cancel out volume
volume × density =
mass
× volume
volume
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
So this will leave us with only mass on the right side.
volume × density =
mass
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
Now we’ll move mass to the left side (click) and volume and density to the right
side. This doesn’t change the equation
mass = volume × density
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
To get the most familiar form of this equation, we’ll switch position of volume and
density (click). Again, this doesn’t change the equation.
mass = density × volume
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
Now that we have the equation for mass,
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
we can substitute values for density and volume into this equation and calculate
the mass.
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
We substitute 7.8 grams per cubic centimeter for the density because that was
given in the question.
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
And we substitute 35 cubic centimeters in for the volume, as that is also given
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
This unit
will
cancel
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
We don’t need to change the unit of volume. It is in cubic centimeters and the density has cubic
centimeters in the denominator of its unit. So the unit cubic centimeters (click) can be cancelled out.
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
Multiplying 7.8 grams per cubic centimeter by 35 cubic centimeters,
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
and cancelling out cubic centimeters,
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
mass = 273 g
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
Gives us a mass of 273 grams.
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
mass = 273 g
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
The whole calculation can be summarized here. Mass is equal to density times
volume
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
mass = 273 g
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
Which is 7.8 grams per cubic centimeter times 35 cubic centimeters
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
mass = 273 g
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
Which comes out to 273 grams.
mass = density × volume
mass =
7.8
× 35 cm3
3
g/cm
mass = 273 g
The mass of a 35 cm3 sample of iron is 273 g
Iron has a density of 7.8 g/cm3. Calculate the
mass of a 35 cm3 sample of iron.
So we can state the final answer as, the mass of a 35 cubic centimeter sample of
iron is 273 grams.