# 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/m^{3}, or g/(cm)^{3}

*m* = mass, in kg or g

*V* = volume, in m^{3} 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/m^{3}. 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 m^{3} for cubical box. The allowed density is ρ = 2 kg/m^{3}. Use the density formula to find mass.

*ρ = m/V*

*m* = ρV

*m* = (2kg/m^{3}) x (5.000 m^{3})

*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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