Blog: The cream in the middle of a cream-filled donut has a volume of 50 cubic centimeters and a mass of 10 grams. What is the density?

Friday, April 16, 2010

The cream in the middle of a cream-filled donut has a volume of 50 cubic centimeters and a mass of 10 grams. What is the density?

Hello!

The density of something, by definition, is the the mass m of this something divided by its volume V:

$\displaystyle\rho$ = m / V.

For heterogeneous objects this is the definition of an average density. For homogeneous substances density doesn't depend on a quantity of a substance used for a measurement. If, say, a volume is increased twice, then the mass will also be twice greater and the density will be the same.

In our case, the density is 10 g / 50 cm^3 = 0.2 $\displaystyle\frac{{g}}{{{c}{{m}}^{{3}}}}.$

A density may be expressed in other units. For example, the standard SI unit is $\displaystyle\frac{{{k}{g}}}{{{{m}}^{{3}}}}.$ Because 1 kg = 1000 g and 1 m = 100 cm, to convert from $\displaystyle\frac{{g}}{{{c}{{m}}^{{3}}}}$ to $\displaystyle\frac{{{k}{g}}}{{{{m}}^{{3}}}}$ it is necessary to multiply by $\displaystyle\frac{{\frac{{1}}{{1000}}}}{{\frac{{1}}{{{100}}^{{3}}}}}=\frac{{{1},{000},{000}}}{{{1},{000}}}={1000}.$