Question

A stone with mass 80.0g was put into a measuring cylinder containing water, if the water level rises by 20.0cm3, calculate the density of the stone. *

Answer 1

volume of water risen= volume of stone

therefore volume of stone= 20cm³

density=weight/volume

=80/20=4g/cm³

Answer 2

The density of the stone is $4\;g/cm^{3}$

• To calculate the density of an object the mass or the weight of the object must be known and the volume of the material is also needed.
• The mass of an object is the amount or the quantity of matter occupied while the volume is defined as the three dimensional space occupied by the object.
• The density of regular materials, that is, for a material with a definite shape like a cuboid or a rectangle etc. its volume can be computed easily using fixed formulae for the shape, given that the mass of the object is already known.
• However, in this case the given object is a stone which is irregularly shaped which means that it does not have a fixed size or shape.
• To find the density of such irregular materials a measuring cylinder is used. The measuring cylinder is used to find out the unknown volume of the stone.
• Here, the mass of the stone is already given to be 80.0 g.
• To find the volume of the stone, the measuring cylinder is first filled with water upto some level.
• The stone is then dropped into the measuring cylinder until it is completely immersed. When the stone is put into the water the water level rises as given in the question.
• The amount of water that the stone displaces is equivalent to its volume as per the Archimedes principle.
• Thus, the volume of the stone is equivalent to the the volume of water that has been risen once the stone as dropped. The risen volume indicates the volume occupied by the stone.

Thus, we know that density is given by:

$Density=\frac{mass}{volume}$

Given,

$Mass=80\;g$

$Volume=20\;cm^{3}$

By substituting these values onto the above equation we get:

$Density=\frac{80}{20}$

$\implies Density=4\;g/cm^{3}$

Thus, this is the density of the stone.

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