Question

Please answer the question fast

Answer 1

Hi there !
Here's the answer:

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¶ $Speed = \frac{Distance}{Time}$

=> Distance = Speed × Time

¶ 1 m = 100 cm

=> 1 cm = 0.01 m

¶ Shape of pipe = Cylinder

¶ Volume of pipe = Volume of Cylinder = $v = Πr^{2}h$

¶ $1 m^{3} = 1000\: litres$

¶ 1 Hr = 60 min = 3600 sec

=> $1 sec = \frac{1}{3600}Hrs$


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SOLUTION :

Given,
Internal Diameter of pipe = d = 7cm

Internal Radius of pipe = r = $\frac{d}{2}$

=> r= $\frac{7}{2}$

=> r = 3.5 cm = 0.035 m


Speed of water = 5 m/s

Now,
Height = h = Distance travelled by water in 60 sec

=> Height = speed × Time

=> h = 5 × 60 = 300 m


Now,

(i)

The Volume of water that flows/discharged from the pipe in 1 min = $Πr^{2}h$

=$\frac{22}{7} × (0.035)^{2} × 300$

= $1.155 m^{3}$

Convert to Litres

= $1155\: litres$


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The volume of water that flows from the pipe in 1 min = 1154 litres


(ii)
Given,
For a rectangular tank,
Length = l = 4 m
Breadth = b = 3m
Height = h = 2.31 m

Capacity of rectangular tank = length × breadth × height

= 4 × 3 × 2.31

= $27.72 m^{3}$

Let the time taken by the pipe to full the tank be ' t ' sec

we know that,
The volume of water that flows from the pipe in 60 sec = 1154 litres

Volume of water that flows from pipe in t sec = $\frac{1.155t}{60} = 0.01925t$

Now,
According to the question,
Volume of water that flows from pipe in t sec = 27.72 sec

=> 0.01925t = 27.72

=> $t = \frac{27.72}{0.01925}$

=> $t = 144000\: sec$

=> $t = \frac{144000}{3600}hrs = 40\: hrs$


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Hope it helps