Density Formula: Meaning, Definition, Solved Examples

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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.

READ HERE  Area Under the Curve Formula with Solved Example

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