# A rock has a density of 4 ml and a mass of 16 gram. What is the volume this rock occupies?

Dec 22, 2016

You have given us the wrong units for density........

#### Explanation:

$\text{Density}$ $=$ $\text{Mass"/"Volume}$, i.e. mass per unit volume, and it typically has units of $g \cdot m {L}^{-} 1$ or $g \cdot c {m}^{-} 3$. If your rock has a VOLUME of $4 \cdot m L$ and a MASS of $16 \cdot g$, then we can take the quotient,

$\text{mass"/"volume}$ $=$ $\frac{16 \cdot g}{4 \cdot m L}$ $=$ $4 \cdot g \cdot m {L}^{-} 1$.

I am being by no means pedantic by calling you out on the question. I realize that everybody makes mistakes, but I don't want you to make a mistake in an exam; and you don't want to make one either.

If you calculate $\text{density}$, the important function to have in the back of your mind is:

$\text{density}$ $=$ $\text{mass"/"volume}$; so units of $g \cdot m {L}^{-} 1$ or $g \cdot c {m}^{-} 3$ are reasonable and rational.

Given TWO of the three properties, we can assign the third, i.e.

$\text{Mass"="Volume"xx"Density}$; $\text{Volume"="Mass"/"Density}$ etc.

When you do these sorts of calculations, if you include UNITS when you work out the quotients and the products, you are building in an internal check on your answer so that you can see you did the right operation. If you calculate a volume and get an answer in $\frac{1}{g}$ you will probably realize that somewhere you made an error. Capisce?