Question

Roof top of a house in a village is rectangular shape of dimensions 22m×20m. The owner has connected drain of roof top with a cylinderical vessel on ground through a circular pipe. so that whole rainwater collected on the roof top can be stored in a cylinderical vessel. The radius of a cylinderical vessel is 50cm. A certain day recorded rainfall is 2.5cm. Find the height of water filled in a cylindrical vessel and volume of water filled in the cylinder.

Answer 1

Area of roof =20*22
=440 sq m
Volume of water =440 *2.5
Volume of cylinder filled with water = π*r squared *h
Total volume =volume of water on roof =volume of water in cylinder
=> 440*2.5 = (22*50*50*h)/7*100*100
=> h= 14m

Answer 2

When doing this kind of question, please remember to convert all the units into the same unit. In this case, I will use meter (m).

So the rainfall is 2.5/100 = 0.025 m
The radius of the vessel = 0.5 m

Total volume of water = 22*20*0.025 = 11 m³
The volume of the vessel is also 11m³ and volume of a cyclinder is V =  2πr²h
 
Using the formula we can find
11 = 2π(0.5)²h
h = 14

So the height of the water is 14 m.