The rain water from a roof of dimensions drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall (in cm).

Let the rainfall be 'x' cm [i.e. 0.01x meters because 1 m = 100 cm ] .


For cylindrical vessel,


Diameter of base = 2 m


Base Radius = 1 m


[As radius = diameter/2]


Height, h = 3.5 m


As we know,


Volume of cylinder = πr2h


Where r is base radius and h is height of cylinder.


So,


Volume of cuboidal vessel = π(1)2(3.5)



Also,


For roof


Length, l = 22 m


Breadth, b = 20 m


Height, h = height of rainfall = 0.01x m


As we know,


Volume of cuboid = lbh


Where l, b and h are length, breadth and height of the cuboid respectively.


Volume of water on roof = 22(20)(0.01x) = 4.4x m3


Given,


Volume of water on roof = volume of cuboidal vessel


4.4x = 11


x = 2.5 cm


Height of rainfall is 2.5 cm.


20