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Q.

Water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how much will the water rise in the tank in half an hour?


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a

78.75 cm

b

85 cm

c

80.75 cm

d

75 cm 

answer is A.

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Detailed Solution

Given that, water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec.
Let rise in water level be h m.
Now, Volume of water through a pipe in 30 minutes = Volume of tank.
Pipe is in form of a Cylinder whose diameter = 2cm.
So,
Radius  = Diameter 2 = 2 2 = 1 cm = 1 100  m  
Now, Rate of filling water is 0.7 m/sec  .  So, in 1 second, water flowing through pipe =0.7 m  .  Given water flowing through a pipe in 30 minutes. So, the water filled is
=0.7×30×60 =1260 m   Thus, height of cylindrical Pipe 1260 m  .
We know that, volume of the cylinder =π r 2 h  .
=π r 2 h =π (1/100) 2 ×1260 =π×1/100×1/100×1260 = π×126 1000 m 3   Let us find the radius of the tank.
r =40 cm = 40 100  m = 4 10  m   Volume of Tank
V =π r 2 h =π× 4 10 2 ×h = 16πh 100 m 3   Volume Of Pipe = Volume of Tank
Question ImageThe height of the water in the tank in half an hour is 78.75 cm.
The correct option is (1).
 
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