Density Formula

Density is a measure of relative compactness, or how heavy an object is relative to its size. Density is defined as mass, m, in a given unit volume, V.

ρ = m/V

ρ = density, kg/m3, or g/(cm)3

m = mass, in kg or g

V = volume, in m3 or (cm)3

Density Formula Questions.

1) You are packing for a trip to Mars. You are given a cubical box to pack that is 1.71 m on a side. Due to fuel and space limitations, the final density, ρ, of your box must be no more than 2 kg/m3. What is the largest mass you can pack?

Answer: The volume, V = (1.71 m x 1.71 m x 1.71 m) = 5.000 m3 for cubical box. The allowed density is ρ = 2 kg/m3. Use the density formula to find mass.

ρ = m/V

m = ρV

m = (2kg/m3) x (5.000 m3)

m = 10 kg

The maximum allowed mass, m, is 10 kilos.

2) If you find a shiny golden rock with a volume of 0.008 (cm)3 and a mass of 0.04 g, is it gold or fool’s gold? The density of gold is 19.3 g/(cm)3 and the density of fool’s gold (iron pyrite) is ~5.0 g/(cm)3.

Answer: For gold, ρ = 19.3 g/(cm)3. The V = 0.008 (cm)3 for this rock. Use the density equation to solve for m, mass of a gold rock. Use the same equation to solve for the mass of a fool’s gold rock.

ρ = m/V

m = ρV

m = 19.3 g/(cm)3 x (0.008 (cm)3 = 0.1544 g for gold

m = 5.0 g/(cm)3 x 0.008 (cm)3 = 0.04 g for fool’s gold.

The mass of the rock you found is identical with the mass of fool’s gold, so you won’t be ‘rich’ today.

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