Question

How to find volume if there is only mass given? Without density.

Answer 1

Hint: Here we will discuss volume, mass, density. Usually, if the density is not given then we can use the density of water i.e. $1g/cc$ as a standard or reference but here only mass is given, so the other way to find volume is the water displacement method. We can do this by experimenting with the help of a measuring cylinder. The amount of water displaced will give the volume of the given object or sample.

Complete step by step answer:
We know that density is equal to mass (m) divided by volume (v) and can be written as \[{{\rho = }}\dfrac{{\text{m}}}{{\text{v}}}\] . Or density is mass per unit volume. If we have the value of any two variables, the third variable can be calculated easily. But in this question only mass is given, so we will use the displacement method to find the volume. Take a measuring cylinder and add the given liquid to it and read the meniscus value which is the\[{{\text{V}}_{{\text{initial}}}}\]. Now submerge the given object into the cylinder and let the object and water settle and read the meniscus again, this will give \[{{\text{V}}_{{\text{final}}}}\] . Now subtract \[{{\text{V}}_{{\text{initial}}}}\] from \[{{\text{V}}_{{\text{final}}}}\] , we will get \[{{\text{V}}_{{\text{object}}}}\] . The \[{{\text{V}}_{{\text{object}}}}\] will be the final volume we need to find out.

Note:
We should be noted that density is an intensive property which does not depend on the amount of matter whereas volume and mass are extensive properties which depend on the amount of matter.Volume is the amount of substance present at a definite temperature and pressure. Mass is the amount of matter in an object. Water displacement method was invented by Archimedes. This method is useful to calculate the volume of irregular solids, for eg, cone, cylinder, etc.