The rain water from a roof af dimensions ` 22 m xx 20 m ` drains into a cylindrical vessel having diameter of bases 2 m and height 3.5 m. If the rain water collected form the roof just fill the cylindrica vessl, them find the rainfull (in cm).

Explanation

Given length of roof =22 m and breadth of roof = 20 m
Let the rainfall be a cm.
`therefore ` Volume of water on the roof `= 22 xx 20xx (a)/(100) = (22a)/(5)m^(3)`
Also, we have radius of base of the cylindrical vessel = 1 m
and height of the cylindrical vessel = 3.5m
`therefore` Volume of the water in the cylindrical vessel when it is just full
`= ((22)/(7) xx 1xx xx(7)/(2)) = 11 m^(3)`
Now, volume of water in the roof = volume of water in the vessel
`rArr " " (22a)/(5)= 11`
`therefore" "a =(11 xx 5)/(22) = 2.5" "[therefore "volume of cylinder"= pi xx ("radius")^(2) xx "height"]`
Hence, the rainfall is 2.5 cm.