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?

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

`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 `g/(cm^3).`


A density may be expressed in other units. For example, the standard SI unit is `(kg)/(m^3).` Because 1 kg = 1000 g and 1 m = 100 cm, to convert from `g/(cm^3)` to `(kg)/(m^3)` it is necessary to multiply by `(1/1000) / (1/100^3) = (1,000,000)/(1,000)=1000.`

So, it is also correct to say that the density of the cream is 200 `(kg)/(m^3).`


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