Question

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

i. Prove that the volume of water falling in a region is proportional to the area of the region.

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

Answer 1

i. The volume of water falling in each square metre are equal.

Let the volume of the rain falling on the 1 square metre be k The volume of the rain falling on the 2 square metre = 2k The volume of the rain falling on the 3 

square metre = 3k 

The volume of the rain falling on the x square metre y = kx Here x and y are proportional.

ii. Let x be the base area of the vessel and h be the height of the water collected, then the volume of water y = xh.

y/x =h

The volume of water collected is different in hollow prisms having different base area.

But \(\frac{volume}{Area}\) is always equal to the height of water level. So the height at which rainwater collected is same.