The density of a material can easily be calculated if we are given the mass and volume of a sample

Calculating Density from

Mass and Volume

In this example, we’re given that a 230 mL sample of butter has a mass of 200 g and we’re asked to calculate the density of butter in grams per centimeter cubed.

A 230 mL sample of butter has a mass of 200 g. Calculate the density of butter in g/cm3.

We know that the formula for density is density equals mass divided by volume.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

The density formula

We’ll make a note of the mass and volume in a table here

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL = 230 cm3

The mass of the sample is 200 g

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL = 230 cm3

And because mL is a unit of volume, we can state that the volume of the sample is230 mL

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL = 230 cm3

However, we notice that they want us to calculate the density in grams per centimeter cubed, or grams per cubic centimeter.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL = 2 cm3

The unit of density required

is g/cm3

So the unit we use for volume needs to be centimeters cubed.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL = = 2 cm3

The unit of density required

is g/cm3

It is known that 1 mL is the same volume as 1 centimeter cubed.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL = = 2 cm3

1 mL = 1 cm3

230 mL = 230 cm3

So 230 mL is the same as 230 centimeters cubed

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL

= 230 cm3

1 mL = 1 cm3

230 mL = 230 cm3

And we can put 230 in for the volume in centimeters cubed.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL

= 230 cm3

1 mL = 1 cm3

230 mL = 230 cm3

Now we can substitute the values for mass and volume into our equation, density equals mass divided by volume

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL= 230 cm3density=

massvolume

We substitute 200 grams in for mass

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL= 230 cm3density=

200 gvolume

And 230 centimeters cubed in for volume

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL= 230 cm3density=

200 g

230 cm3

So the density is 200 grams divided by 230 centimeters cubed,

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL= 230 cm3density=

200 g

230 cm3

Which comes out to 0.87 grams per centimeter cubed.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL= 230 cm3density=

200 g

230 cm3

density=0.87 g/cm3

So the answer to the question is the density of butter is 0.87 grams per centimeter cubed.

A 230 mL sample of butter has a mass of 200 g.Calculate the density of butter in g/cm3.

density=mas

svolume

mass 200 g

volume230 mL= 230 cm3density=

200 g

230 cm3

density=0.87 g/cm3

The density of butter is 0.87 g/cm3

Answer