Q. 194.5( 15 Votes )
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.
Volume of cuboidal vessel = π(1)2(3.5)
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
Volume of water on roof = volume of cuboidal vessel
4.4x = 11
x = 2.5 cm
Height of rainfall is 2.5 cm.
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