This is a question of density. Which of these two blocks would be heavier? One is made of lead and the other is made of cork (that’s the same cork that is used to seal wine bottles.)

#### The Explanation

Density is the term that we can use to describe how much mass is packed into a unit volume of a substance. A unit volume just means a volume that is equal to 1 cm^{3} or 1 m^{3}. So when we talk about the density of a substance we are talking about how much mass can fit into a volume of 1 cm^{3} or 1 m^{3}.

Let’s go back to the example above.

The block of lead has a mass of 11.3 g packed into a volume of 1 cm^{3}. Therefore the density of lead is 11.3 g/cm^{3}.

Similarly the density of the cork is 0.25 g/cm^{3} because it has 0.25 g of mass packed into a unit volume of 1 cm^{3}.

#### The Equation

We can write density in the form of an equation \( density = {mass \over volume} \). In symbol form it is \( ρ = {m/ V} \)

#### The Units

To get the unit of density consider the units of the other quantities you are dividing.

\( ρ = {mass \over volume} {the\ unit\ of\ mass\ is \over the\ unit\ of\ volume\ is} {kg \over m^3} \)Therefore the resulting unit of ρ is \(kg\over m^3\) or \( kgm^{-3}\)

Where the mass is in g and the volume is in cm^{3} the resulting unit of ρ will be \(g\over cm^3\) or \( gcm^{-3}\)

#### Examples

Find the density of a block if a mass of 13 kg has a volume of 5 m^{3}.

m = 13 kg

V = 5 m^{3}

\( ρ = {13 \over 5 } {kg \over m^3}\)

\( ρ = {2.6} \ {kgm^{-3}} \)

Determine the volume of lead that has a mass of 110 g. The density of lead is known to be 11.3 g/cm^{3}.

m = 110 g

ρ = 11.3 g/cm^{3}

V = ?

\( ρ = {m \over V} \)Rearranging the equation to make V the subject gives

\( V = {m \over ρ}\)\( V = {110 \over 11.3} {g \over gcm^{-3} } \)

\( V = 9.7 cm^3 \)

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