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# The rain water from a roof of dimensions 22 m x 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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This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
The rain water from a roof of given dimensions drains into a cylindrical vessel having diameter of base 2 m and height; 3.5 m. find the rainfall in cm.
This is the Question Number 05, Exercise 17.5 of M.L Aggarwal.

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1. Given dimensions of the cylindrical vessel = 22 m × 20 m

Let the rainfall be x cm.

Volume of water = (22×20×x)m3

Diameter of the cylindrical base = 2 m

So radius of the cylindrical base = 2/2 = 1 m

Height of the cylindrical base, h = 3.5 m

Volume of cylindrical vessel = r2h

= (22/7)×12×3.5

= 11 m3

Since the rain water collected from the roof just fill the cylindrical vessel, the volumes are equal.

22×20×x = 11

x = 11/22×20

= 1/40 m

= (1/40)×100 cm

= 2.5 cm

Hence the rainfall is 2.5 cm.

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