• Where “m” is the mass of the material measured in kilograms (kg)
• “V” is the volume measured in metres cubed (m3) 
• “ρ” is the density measured in kilograms per metre cubed (kg/m3) 
• Smaller unit of density is grams per centimetres cubed (g/cm3).

Density Calculation

Q: An object has a mass of 1200 kg and a volume of 3 m3. What is its density, in kg/ m3?

Volume Calculation

Liquid water has a density of 1000 kg/m3.  Calculate the volume occupied by a mass of 500 kg.

Mass Calculation

Q: What is the mass of the volume of 6 m3 of a rock of density 2000 kg/m3?

Density of a Regular Solid Object

• Measure the mass of the solid object (rectangular blocks) using an electronic top-pan balance.
• Measure to the nearest centimeters the dimensions of the regular-shaped solid (length, width, height) using a ruler.
• Calculate the volume of the block by using the formula V = l × w × h
• Finally, calculate the density of the solid object with the help of the formula.

• Some liquids are thinner, and some are thicker, so they have different densities. 
• Their densities can be calculated in the laboratory through experiments.
• To calculate the density, measure the mass of the empty measuring cylinder/beaker using a top-pan balance.

• Add some amount of liquid to the measuring cylinder and record its volume from the scale marked on it.
• Record the mass of the empty cylinder with the help of a top-pan balance to the nearest gram, say m1.
• Measure the total mass of the cylinder + liquid mass, say mass m2.
  
• The following relationship can Calculate the mass m of the Liquid

m = m2 – m1

• The density of the liquid can be calculated by using the following formula.

Q: The diagram shows an experiment to find the density of a liquid. What is the density of the liquid?

• Measure the volume V1 of a certain amount of liquid by using a measuring cylinder.
• Tie the solid object with a fine thread and dip it gently into the liquid, and measure volume V2 of the liquid plus the volume of the solid object.

Volume of solid, (V) = V2-V1

• Measure the mass “m” of the solid object by using a top-pan balance to get density.

Q: A student wants to calculate the density of an irregular piece of metal having a mass of 44 g.

The following figures show the volume of water in both measuring cylinders. Calculate the density of the metal.

4.3 Floating and Sinking depend on Density

Different Objects have different Densities

If you take the same volume of different substances, it is not necessary that they have the same amounts of mass.

Density of Helium 

A helium-filled balloon moves upwards because the density of the helium gas is less than the density of air.

Density of Wood 

The density of the wood is less than the density of water, so it keeps on floating on the surface of the liquid.

Density of Metals

The density of a metal object is more than the density of water, so when we keep it at the top surface of the water, it sinks into the water.