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?

Answer 1

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.