Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?
Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

NCERT Exemplar Class 10 Maths Chapter 12 Ex. 12.4 Question 8

Let the time taken by line to fill lake = t hours

Water streams 15 km in 60 minutes, in this way, it will stream 15t meters in t hours.

We realize that,

Volume of cuboidal lake up to tallness 21 cm = Volume of water that goes through pipe in “t” hours

Thinking about cuboidal lake,

Length, l = 50 m

Broadness, b = 44 m

Stature, h = 21 cm = 0.21 m

We realize that,

Volume of tank = lbh

Volume of water \[=\text{ }50\left( 44 \right)\left( 0.21 \right)\text{ }=\text{ }462\text{ }m3\]

Thinking about round and hollow line

Base width = 14 cm

Base span, r = 7 cm = 0.07 m

Stature, h = 15t km = 15000t m

We likewise realize that,

Volume of a chamber = πr2h

Volume of water passed in pipe

\[=\text{ }\pi \left( 0.07 \right)2\left( 15000t \right)\]

\[=22/7\text{ }\times \text{ }0.07\text{ }\times \text{ }0.07\text{ }\times \text{ }15000t\]

= 231t cm3

Thus, we have

231t = 462

t = 2 hours

Time needed to top tank off to a tallness of 25 cm is 2 hours.