A housing society used to collect rain water from the foof of its building `22 m xx 20 m` to a cylindical vessel having diameter of base 2 m and height 3.5 m and them poump this water into the main water tank so that all members can use it. On a particular day the rain water collected from the roof just filled the cylindrical vessel. Then, find the rain water collected from the roof just filled the cylindrical vessel. Then, find the rainfall in centimetre.

Explanation

Length of the foof = 22 m. Breadth of the roof = 20 m.
Let the rainfall be x cm.
Volume of water on the roof
`=-(22xx20xxx/100)m^(3)=((22x)/5)m^(3)`.
Radius of the cylindrical vessel, r = 1 m.
Height of the cylindrical vessel, h = 3.5 m.
Volume of water in the cylindrical vessel when just full
`=pir^(2)h=(22/7xx1xx1xx7/2)m^(3)=211m^(3)`.
Now, volume of water on the roof = volume of water in the cylindrical vessel
`rArr" "(22x)/5=11rArrjx=((11xx5)/22)=2.5`.
Hence, the rainfall is 2.5 cm.