Question

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=>Water flows at the rate of 10 meters per minutes through a cylindrical pipe 5mm in diameter.How long would it take to fill a conical vessel whose diameter at the surface 40 cm and depth 24 cm ?

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Answer 1

Answer:

51.2

Step-by-step explanation:

For cylindrical pipe:

Diameter d = 25 mm.

Radius r = (d/2) = 2.5 mm = 0.25 cm

Rate of water flow h = 10m/min

                                     = 1000 cm/min.

(For conical vessel:

Diameter = 40 cm.

Radius r = d/2 = 20 cm.

Depth = h = 24 cm.

Let the conical vessel be filled in 'x' minutes.

Volume of water flowing through cylindrical pipe in x mins = volume of conical vessel.

⇒ πr²h * x = (1/3)πr²h

⇒ (0.25)² * 1000 * x = (1/3) * (20)² * 24

⇒ x = (400 * 8)/62.5

⇒ x = 51.2.

Therefore, it will take 51.2 minutes to fill the vessel.

Hope it helps!

Answer 2

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm

Speed of water = 10 m/min = 1000 cm/min

Volume of water that flows in 1 minute = Π r2 h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm3

Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm

Therefore, Capacity of the vessel = 1/3 x Π r2 h

= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm3

Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute

= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec