Question

Water flows out through a circular pipe whose internal
diameter is 2 cm, at the rate of 6 meters 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?
​

Answer 1

Answer:

Given diameter of the circular pipe = 2 cm

So, the radius of the circular pipe = 2/2 = 1 cm

Height of the circular pipe = 0.7 m = 0.7 * 100 = 70 cm

Now, volume of the water flows in 1 second = πr2 h

= 3.142 * 12 * 70

= 3.142 * 70

Volume of the water flows in 1/2 hours = 3.142 * 70 * 30 * 60

Now, volume of the water flows = Volume of the cylinder

=> 3.142 * 70 * 30 * 60 = πr2 h

=> 3.142 * 70 * 30 * 60 = 3.142 * (40)2 h

=> 70 * 30 * 60 = 40 * 40 * h

=> h = (70 * 30 * 60)/(40 * 40)

=> h = (70 * 3 * 6)/(4 * 4)

=> h = 1260/16

=> h = 78.85 cm

So, the level of water rise in the tank in half an hour is 78.75 c

Answer 2

Answer:

EXPLANATION.

Water flows through a circular pipe.

Internal diameter = 2 cm.

Rate = 6m/sec into a circular tank.

The radius of whose base = 60 cm.

To find the rise in the level in water in 30 minutes.

As we know that,

Diameter = 2 x Radius.

Radius = Diameter/2.

Radius = 2/2 = 1 cm = 1/100 m.

Volume of cylinder = πr²h.

Volume of water flows through a circular pipe in 1 seconds = πr²h.

π x (1/100)² x 6.

The raise in the water level in 30 minutes = π x (1/100)² x 6 x 30 x 60.

Radius whose base = 60 cm = 60/100 m.

Volume = πr²h.

⇒ π x (60/100)² x h.

⇒ π x (60/100)² x h = π x (1/100)² x 6 x 30 x 60.

⇒ 60/100 x 60/100 x h = 1/100 x 1/100 x 6 x 30 x 60.

⇒ 60 x 60 x h = 6 x 30 x 60.

⇒ 60 x h = 6 x 30.

⇒ 10 x h = 30.

⇒ h = 3m.