# Question #37fe4

##### 1 Answer

Here's what I would try.

#### Explanation:

Let's say that the sample that is too big to fit in the graduated cylinder has a volume

By definition, the **density** of the mineral, *mass* of **any sample** of this mineral and the *volume* it occupies.

So for the initial sample, you have--I'll skip the *units* for simplicity

#rho = M/V" "" "color(darkorange)("(*)")#

Now, cut a piece of this sample that is small enough to fit in a graduated cylinder. Place this small piece on a scale and record its mass, let's say

Use the graduated cylinder to determine its volume.

Let's say that this small piece has a volume

Since the **density** of the mineral must be the same *regardless* of the mass of the sample and the volume it occupies, you can say that--I'll skip the *units* for simplicity

#rho = m/v#

You can now use equation

#M/V = m/v#

Rearrange to find **initial sample**

#M/V = m/v implies V = (Mcolor(red)(cancel(color(black)("g"))))/(mcolor(red)(cancel(color(black)("g")))) * vcolor(white)(.)"mL"#

#V = (M/m * v)color(white)(.)"mL"#

And there you have it, the volume of the initial sample as a function of its mass