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Question
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.
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 = `22 xx 20 xx a/100 = (22a)/5 m^3`
Also, we have radius of base of the cylindrical vessel = 1 m
And height of the cylindrical vessel = 3.5 m
∴ Volume of water in the cylindrical vessel when it is just full
= `(22/7 xx 1 xx 1 xx 7/2)`
= 11 m3
Now, volume of water on the roof = Volume of water in the vessel
⇒ `(22a)/5` = 11
∴ a = `(11 xx 5)/22` = 2.5 ...[∵ Volume of cylinder = π × (radius)2 × height]
Hence, the rainfall is 2.5 cm
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