Solved Examples on Density Formula

Example 1: Find the density of seawater if 1120 kg of water occupies 1m³.

Solution:

Given,

Mass of water = 1120 Kg

Volume occupied by the water = 1 m³

The density formula is,

Density = Mass/Volume

ρ = 1120/1 
   = 1120 kg/m³

Example 2: If a rock sample has a high carbon content and a volume of 0.055 cm³ and a mass of 0.25 g. Check whether it is Graphite or Diamond if the density of graphite is 2.266 g/cm³ and the density of diamond is 3.51g/cm³.

Solution:

Given,

Volume of rock = 0.055 cm³

Mass of the rock = 0.124 g

Density of Graphite = 2.266 g/cm³

Density of Diamond = 3.51 g/cm³

Density of Rock (ρ) = m/V
                               = 0.124/0.055

Density of Rock (ρ) = 2.25 g/cm³

The density is similar to graphite (2.266 g/cm³) thus the rock is Graphite.

Example 3: You’re preparing to travel to Mars. You’ve been given a 1.34-meter-long cubical box to pack. Your box’s final density must be no more than 5 kg/m³ due to fuel and space constraints. What is the maximum weight you can carry?

Solution:

Given,

A cubical box of 1.34 m in length

Volume of cubical box = 1.34 m × 1.34 m × 1.34 m 
                                     = 2.4061 m³,

Density (ρ) = 5 kg/m³

Density(ρ) = mass(m)/volume(V)

m = ρ × V

m = 5 × 2.4061

mass of the cubical box = 12.0305 kg 
                                       ≅ 12 kg

Example 4: What is the density of a sugar cube that weighs 30 grams and has a side length of 8 cm?

Solution:

Given,

Mass of sugar cube = 30 g, 

Volume of sugar cube = 8 cm × 8 cm × 8 cm 
                                    = 512 cm³

ρ = m/V

ρ = 30/512

ρ = 0.0585 g/cm³

Density is defined as the measurement of the weight of the object when a fixed volume of it is taken. It can be calculated by dividing the mass of an object by its mass. It is the true measure of the heaviness of the material. This can be understood with the help of the following example,

“Which weighs heavier 1 kg of cotton or 1 kg of iron?” The obvious answer to this is iron is heavier than cotton so 1 kg of iron must be heavier than 1 kg of cotton but here, both of them weigh exactly the same (1 kg) but iron feels heavier because of the density as the density of Iron is heavier.

In this article, we have provided everything related to what is density, the formula for density, density of water, and how to calculate density.