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
Solution:
Given, water is flowing at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide.
We have to find the time at which the level of water in the pond rise by 21 cm.
Volume of cylindrical pipe = πr²h
Given, diameter = 14 cm
Radius = 7 cm
1 m = 100 cm
Radius = 7/100 = 0.07 m
Rate of flow = 15 km/hr
1 km = 1000 m
Rate of flow = 15(1000) m/hr
= 15000 m/hr
Volume of water flowing through the cylindrical pipe in one hour = (22/7)(7)²(15)
= (22/7)(0.07)²(15000)
= 1617/7
= 231 m³
Volume of cuboidal pond = length × width × depth
Given, length = 50 m
Width = 44 m
Depth = 21 cm
1 m = 100 cm
Depth = 21/100
= 0.21 m
Volume of pond = 50 × 44 × 0.21
= 462 m³
Now, time taken by the pipe to fill the pond with water to a height of 21 cm = volume of pond/volume of water flowing through the pipe in one hr
= 462/231
= 2 hr
Therefore, the time taken by the pipe to fill the pond with water upto 21 cm is 2 hours.
✦ Try This: Water is flowing at the rate of 25 km/h through a pipe of diameter 22 cm into a cuboidal pond which is 60 m long and 54 m wide. In what time will the level of water in pond rise by 50 cm?
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13
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NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 8
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
Summary:
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. The level of water in the pond rose by 21 cm in 2 hours
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