Question
Wed March 30, 2011 By: Sagar Kumar
 

The rain water collected on the roof of a building of dimension 22 m × 20 m is drained into cylindrical vessel having base diameter 2 m and height 3.5 m. If the vessel is fill up to the brim, find the height of rain water on the roof.

Expert Reply
Thu March 31, 2011
Dear Student,
 
Here is the solution:
 
r = radius of cylindrical vessel =  1 m
h = height of cylindrical vessel = 3.5 m
 
Therefore volume of cylindrical vessel = 22/7 x 1x 3.5 m3 = 11m3
 
Let the rain fall be y m. Then
 
Volume of water on roof = volume of cuboid of base 22m x 20m and height ym
                                 = (22 x 20 x y) m3
Now volume of water on roof = volume of water in cylinder
=> (22 x 20 x y) = 11
y = 11 /(22 x 20)
   = 1/40 m
   = 100/40 cm
   = 2.5 cm
 
Therefore height of water on roof = 2.5 cm
 
 
Regards
Team topperlearning 
 
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