Question

find the Diameter of the pipe​

Answer 1

$<b><u>Solution:-$

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.

Answer 2

$\Huge\blue{\textbf{Solution:}}$

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.