I need help with this

Question

What is the mass,in grams,of a pure iron cube that has a volume of 5.00cm ^3

Answer 1

Hi Yenesky!

The relationship between mass and volume is density, which is mass per volume. Looking up iron's density, we find that it's 7.87 g/cm³.

Let's pick this problem apart. They're asking for the mass which is an amount of substance, which can be represented by g, or anything similar. We know that density represents mass / volume, in units of g/cm³ or anything similar. Meanwhile, we have a volume of iron, V, and iron's density, ρ (that's the Greek letter for r, rho. Don't mind that it looks like a p.):

V = 5.00 cm³

ρ = 7.87 g / cm³

We see that cm³ is on the bottom of density so how can we remove that to be left with only grams, g? Well, we know that since density is mass / volume, and we're trying to find mass, let's set up our equation and solve for mass, m:

m / V = ρ ; multiply both sides by V

m = ρ * V ; the V's cancel out on the left side

So now, we can plug in our values:

m = 7.87 g/cm³ * 5.00 cm³

= 39.35 g

≈ 39.4 g (remember sig fig rules for multiplication)

So there you have it! Please reach out if you have any further questions.

And if you'd like to know why ρ is used for density instead of an English r, or even better a D, Greek philosopher, Archimedes, and others after studied densities of Regions (3-D), Surfaces (2-D), and Lines (1-D) - so they used their language's letters for r, s, and l: ρ (lowercase rho), σ (lowercase sigma), and λ (lowercase lambda).