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Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour

Solution:

Given, water flows through a cylindrical pipe with inner radius 1 cm at the rate of 80 cm/sec in an empty cylindrical tank with base radius 40 cm.

We have to find the rise of the water level in the tank in half an hour.

Volume of cylinder = πr²h

Given, r = 1 cm

Rate of flow = 80cm/sec

Volume of water that flows through a cylindrical pipe = (22/7)(1)²(80)

= 251.429 cm²/sec

1 hour = 60 minutes

1 minute = 60 seconds

Volume of water flows through pipe in 30 minutes = 251.429 × 30 × 60

= 452571.429 cm³

Volume of cylindrical tank = πr²h

Given, r = 40 cm

= (22/7)(40)²h

= 5028.571h cm³

Given, volume of water flowing through the cylindrical pipe in 30 minutes = volume of water in the cylindrical tank

5028.571h = 452571.429

h = 452571.429/5028.571

h = 90 cm

Therefore, the rise of water level in the tank is 90 cm.

✦ Try This: Water flows through a cylindrical pipe, whose inner radius is 2 cm, at the rate of 60 cm/sec in an empty cylindrical tank, the radius of whose base is 30 cm. What is the rise of water level in a tank in an hour?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 18

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour

Summary:

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. The rise of the water level in the tank in half an hour is 90 cm

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