How can you solve for a derived unit involving density?

I don't know what you mean. Density is a derived unit, no mater what the units used are. Do you have an example of what you are doing?

Yes. What is the mass of a sample of material that has a volume of 55.1 cm^3 and a density of 6.72 g/cm^3? D= m/v. I thought that it may be derived unit because of the grams.

If you draw out a factor label table, it may help.

Mass/velocity=kilogram/distance=kg/d/time=kg*t/d=kgt/d=kgs/m

To solve for the mass of a sample of material, given its volume and density, you can use the formula:

density = mass / volume

In this case, you are given the volume of the sample as 55.1 cm³ and the density as 6.72 g/cm³. You need to rearrange the formula to solve for mass.

1. Start by plugging in the given values into the formula:

6.72 g/cm³ = mass / 55.1 cm³

2. To solve for mass, multiply both sides of the equation by the volume:

(6.72 g/cm³) * 55.1 cm³ = mass

3. Calculate the product on the left side of the equation:

370.992 g = mass

Therefore, the mass of the sample of material is 370.992 grams.

Drawing out a factor label table can also be helpful in keeping track of the units and cancelling them appropriately. The factor label table would look like this:

Given: volume = 55.1 cm³, density = 6.72 g/cm³
To find: mass = ?

Conversion Factors:
1 cm³ = 1 mL
1 g = 1 cm³

Work:
mass (grams) = density (g/cm³) * volume (cm³)
mass = 6.72 g/cm³ * 55.1 cm³
mass = 370.992 g

The factor label table helps ensure that the units cancel out correctly, and you end up with the desired unit (grams in this case).