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Question 19
The rain water from a roof of dimensions 22 m, 20 m 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.

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Solution

Given, length of roof = 22 m and breadth of roof = 20 m.
Let the rainfall be a cm.
Volume of water on the roof = 20×22×a100=22a5 m3
Also, we have radius of base of the cylindrical vessel = 1 m
And height of the cylindrical vessel = 3.5 cm
Volume of water in the cylindrical vessel when it is just full
[Volume of cylinder=π×(radius)2×height]
=(227×1×1×72)=11 m3
Now, volume of water on the roof = Volume of water in the vessel
22a5=11
a=11×522=2.5
Hence , the rainfall is 2.5 cm.


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