# Density Formula

What is Density?

The density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object. Thus, we can define density of an object as its mass per unit volume. It is a unique physical property for a particular object. It is denoted by the Greek letter ρ (rho). Mathematically, density of an object can be expressed as below:

$Density= \frac{Mass}{Volume}$

$\rho = \frac{m}{v}$

Though its SI unit is kg/m³, for convenience we use g/cm³ for solids, g/ml for liquids and g/L for gases. Density can be explained as the relationship between the mass of the substance and volume it takes up. In a qualitative term, it shows how much heavy an object is at constant volume. Different substances have different density, which means for the same volume of different substances weigh differently.

Generally the density of water is taken as standard value for calculating the density of substances. If a substance is less dense then it will float on water while it will sink in case of high dense than water. The density of water is around approximately about 1 gram/cubic centimeter.

Density in Real Life:

Many applications of density are there in our real life like a few examples are in pipe design, ship building, helium balloons, weight distribution in the airplane and the fact that ice floats on water.

• The knowledge of densities of two substances helps you in separation techniques. For example, separation of oil from water. Leakage of oil tank in the ocean then oil drops starts to float on the water due to their less density in the water.

• Another well-known application of density is determining whether an object will float on water or not. Floating of ships and diving of submarines are due to their density difference.

Solved Examples:

Question 1: Take two boxes which have same volume. Fill the first box with x balls and the second box with 6x balls. If the mass of each ball is same, which box would weigh more?

Solution: The box that has more balls has more mass per unit of volume.

Here the first box contains x number of balls and second box contains 6x number of balls. Since the number of balls in the second box is 6 times the first box, second box would weigh more. This property of matter is called density.

Question 2: Calculate the density of water if it has mass of 1160 Kg and volume of 1m3?

Solution: Given,

Mass = 1160 Kg

Volume = 1m3

Density is given by the formula:

Density = Mass/Volume

ρ = 1160/1 = 1160 kg/m3

Questions 3: If you find a shiny rock, a carbon allotrope with a volume of 0.042cm³ and a mass of 0.14 g, is it graphite or diamond? The density of graphite is 2.266 g/cm3 and the density of diamond is 3.51g/cm3.

Solution: Given,

Volume of the shiny rock =0.042cm³

Mass of the shiny rock = 0.15 g

Density of graphite = 2.266 g/cm3

Density of diamond = 3.51g/cm3

Use the density equation to solve for m, mass of graphite and for the mass of a diamond.

ρ = m/V

m = ρV

m = 2.266 g/cm³ x 0.042cm³ = 0.0951g for graphite

m = 3.51g/cm3 x 0.042cm³ = 0.1474 g for diamond

The mass of the shiny rock you found is identical with the mass of diamond.

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