During rainfall, the volume of water falling in each square metre may be considered equal.

Explain why the heights of rainwater collected in different sized hollow prisms kept near one another are equal.

Let us consider two hollow prisms kept near to one another with different base.

We can think of random number of water columns inside these prisms. Let the base of these columns be squares of area 1cm².

Then each water column will be a square of prism of base area 1cm².

We have seen in above part, that the heights of all water prisms be equal. Regardless of whether they are in the first hollow prism or second hollow prism.

Let the height be h.

Let the base area of first prism = a₁

Let the base area of second prism = a₂

Then total number of water prisms (each with base area 1cm²) in first prism

Then total number of water prisms (each with base area 1cm²) in second prism

All the a₁ and a₂ in the first prism and second prism will have the same heights h.

That means, the water level in both prism will be h.

So, whatever number of hollow prism (of different base sizes) we place near one another, after the rainfall, the height of water in all will be the same.

Consider two paddy fields in a locality. Let their areas be a₁ and a_2. If the water is allowed to run off and if there is no sewage into the ground, there will be two water prisms. Each will cover the entire area of the respective field.

The volume of first field = v₁ = a₁h

The volume of second field = v₂ = a₂h

h is a constant. So, if area increases, volume increases and if area decreases, volume decreases.

That means volume is proportional to the area.