Question

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Water flows through a circular pipe whose internal diameter is 2 cm at the rate of 6 m/sec into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level in water in 30 minutes

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Answer 1

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.

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.