Q2 of 18 Page 213

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

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

Let us consider a surface with three squares of height h and side 1m on a region.


On this surface, we can mark a random number of squares, each side of side 1m. So, each of such squares will have an area of 1m2.


It is stated in the question that, “the volume of water falling in each square metre may be considered equal”.


So, each of the three squares will receive equal volume of water.


If this water is not allowed to sun off and if there is no sewage into the ground, the water received will become a water column. There will be three water columns.


These water columns are prism with square base. And they have the same volume (V), because, according to volume of water in each square should be considered equal.


We know that,


Volume = base area × height


But base area of all prism = 1m2


⇒ V = 1 × h


⇒ V = h


But V is same for all three prisms.


More from this chapter

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