Math, asked by SmritiG596, 10 months ago

Water flows out through a circular pipe whose internal diameter is 2 cm. at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

Answers

Answered by aksarkumar80
1

Answer:

Step-by-step explanation:

The volume of the water that flows out through the circular pipe of radius 1cm, at the rate of 6 metres per second, in one second is same as the volume of a cylinder of radius 1cm and height=6 metres.

Therefore,

volume of the water that flows out through the circular pipe in 1 second=

2 3

22/7 × (1/100) × 6m

=> volume of the water that flows out through the circular pipe in 30 minutes

3

22/7 × 1/10000×6×30×60m

let the water level rise to a height of 'h' metres in 30 minutes in the cylindrical tank of base radius 60cm. Then,

Volume of the water collected in the tank in 30 minutes=

2

22/7 × (60/100) × h

Therefore,

2

22/7×(60/100)×h= 22/7×1/10000×6×30×60

=> 3m

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Answered by nikitasingh79
2

Given : Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 m/s into a cylindrical tank and the radius of base is 60 cm.  

Internal diameter of circular pipe = 2 cm

Internal radius of circular pipe ,r = 2/2 = 1 cm

r = 1 cm = 1/100 m  

[1 cm = 1/100 m]

Rate of flow of water through pipe = 6 m/s

Length of pipe ,h = 6 m

Radius of base of cylindrical tank ,R = 60 cm

R = 60 cm = 60/100 m

So, volume of the water that flows through the circular pipe in 1 second = πr²h  

= 22/7 × (1/100)² × 6 m³

Volume of the water that flows through the circular pipe in 30 min (30 × 60) second =  22/7 × (1/10000) × 6  × 30 × 60 m³

Let the water level rise to a height of H metres in 30 minutes in the cylindrical tank of base radius 60 cm.  Then,  

Volume of the water collected in the tank in 30 minutes = πR²H   22/7 × (60/100)² × H m³

The volume of water that flows out through the circular pipe of radius 1 cm at the rate of 6 m/s in 1 second is same as the volume of a cylinder of radius 1 cm and height 6 m :

22/7 × (1/10000) × 6  × 30 × 60  = 22/7 × (60/100)² × H

22/7 × (1/10000) × 6  × 30 × 60  = 22/7 × 60 × 60 × 1/10000 ×H

6 × 30 = 60 H  

H = (6 × 30)/60

H = 30/10

H = 3 m  

Hence, the rise in the level of water in 30 minutes is 3 m.

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