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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration
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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.
Solution:
Although the water is transferred from cuboidal roof to cylindrical vessel, its volume remains the same.
Given dimensions of the roof = 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 =π 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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