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Question
500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04m3?
Solution
Let the rise of water level in the pond be hm, when 500 persons are taking a dip into a cuboidal pond.
Given that,
Length of the cuboidal pond = 80 m
Breadth of the cuboidal pond = 50 m
Now, volume for the rise of water level in the pond
= Length × Breadth × Height
= 80 × 50 × h
= 4000h m3
And the average displacement of the water by a person = 0.04 m3
So, the average displacement of the water by 500 persons = 500 × 0.04 m3
Now, by given condition,
Volume for the rise of water level in the pond = Average displacement of the water by 500 persons
⇒ 4000h = 500 × 0.04
∴ h = `(500 xx 0.04)/4000`
= `20/4000`
= `1/200 "m"`
= 0.005 m
= 0.005 × 100 cm
= 0.5 cm
Hence, the required rise of water level in the pond is 0.5 cm.
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