Question

Water is flowing at the rate of 2.52 km per hour through a cylindrical pipe into a cylindrical tank the radius of whose base is 40 cm if the increase in the level of water in the tank in half an hour is 3.15 m find the internal diameter of the pipe

Answer 1

Answer:

Step-by-step explanation:

Given:

Height of increased water level h = 3.15 m = 315 cm

Radius of the water tank, r = 40 cm

Volume of water that falls in the tank in half an hour = πr2h

= π × (40)2 × 315

= 5,04,000 π cm3

Rate of flow of water = 2.52 km/h

Length of water column in half an hour = 2.52 ÷ 2 = 1.26 km = 1,26,000 cm..

We assume that the internal diameter of the cylindrical pipe is d.

Volume of the water that flows through the pipe in half an hour =

We know that,

Volume of the water that flows through the pipe in half an hour = Volume of water that falls in the tank in half an hour..

Thus, the internal diameter of the pipe is 4 cm.

Hope it helps

Answer 2

Here is your answer ⤵⤵⤵

Increase in the water level in half an hour = 3.15 m = 315 cm

Radius of the water tank = 40 cm

Volume of the water that falls in the tank in half an hour = πr²h

= 22/7*40*40*315

= 1584000 cu cm

Rate of the water flow = 2.52 km/hr

Length of water column in half an hour = (2.52*30)/60

= 1.26 km = 126000 cm

Let the internal diameter of the cylindrical pipe be d.

Volume of water that flows through the pipe in half an hour = π*(d/2)²*126000

As we know that, 

Volume of the water that flows through pipe in half an hour = Volume of water that falls in the cylindrical tank in half an hour

⇒ 22/7*(d/2)²*126000 = 1584000

⇒ 22/7*d²/4*126000 = 1584000

⇒ d² = 16

⇒ d = √16

⇒ d = 4

So, the internal diameter of the pipe is 4 cm Answer.

HOPE IT HELPS YOU ☺☺ !!