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Question
The rain water from a 22 m × 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills `4/5` th of the cylindrical vessel, then find the rainfall in centimetre.
Solution
We have,
the lenghth of the roof, l = 22 m,
the width of the roof , b = 20 "m"
the base radius of the cylindrical vessel, `"R" = 2/2 =1 "m"`
the height of the cylindrical vessel, H = 3.5 m
Let the height of the rainfall be h.
Now,
Volume of rainfall = Volume of rain water collected in the cylindrical vessel
`rArr "lbh" = 4/5xx "Volume of cylindrical vessel"`
`rArr 22xx 20xxh =4/5xxpi"R"^2"H"`
`rArr 440"h" = 4/5 xx 22/7xx1xx1xx3.5`
`rArr "h" = 4/5xx22/7xx3.5/440`
`rArr "h" = 0.02 "m"`
∴ h =2 cm
So, the height of the rainfall is 2 cm.
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