Density is a measure of how tightly the mass of an object is packed into the space it takes up.
It can be calculated by dividing mass by volume.
\({density} = \frac{mass}{volume}\)
Or
\({d} = \frac{m}{v}\)
Example
Calculate the density of an object with a mass of \({600 g}\) and a volume of \({800~ cm}^3\).
\({d} = \frac{m}{v} = \frac{600}{800} = {0.75}\)
The object will have a density of \({0.75~g/cm}^3\)
The units for density are \({g/cm}^3\) or \({kg/m}^3\).
They are compound units as they are a combination of two units.
Question
A glass marble with a volume of \({6.85~cm}^3\) has a mass of \({20~g}\).
Calculate the density, to \({1}\) decimal place, of the glass marble.
Answer
\({d} = \frac{m}{v} = \frac{20}{6.85} = {2.9}\)
The marble will have a density of \({2.9~g/cm}^3\).
Rearranging the formula for density
Rearranging the formula for density enables us to calculate the mass, given the density and the volume, or to calculate the volume, given the density and the mass.
\({d} = \frac{m}{v}\)
\({m} = {d}\times{v}\)
\({v} = \frac{m}{d}\)
The triangle can help you rearrange the formula.
Example
What is the volume of a piece of metal that has a mass of \({42~kg}\) and density of \({6000~kg/m}^3\)?
\({v} = \frac{m}{d} = \frac{42}{6000} = {0.007~m}^3\)
Question 1
A model of an Egyptian pyramid is made from plastic with a density of \({1.3~g/cm}^3\) .
The volume of the pyramid is \({100~cm}^3\).
What is the mass of the model?
Answer
\({m} = {d}\times{v}\)
\({m} = {1.3}\times{100} = {130~g}\).
The mass of the model is \({130~g}\).
Question 2
A wooden stick has a mass of \({9~g}\) and a volume of \({12~cm}^3\).
Find the density of the wood.
Answer
The density of the wood is \({0.75~g/cm}^3\).
Question 3
Olympics medals have a volume of \({8.5~cm}^3\) .
Gold has a density of \({19~g/cm}^3\).
Calculate the mass of a gold medal.
Answer
The mass of the gold medal is \({161.5~g}\).
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