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Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm ?
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- 51 min 12 s
- 52 min 1 s
- 48 min 15 s
- 55 min
Correct Option: A
Given, radius of pipe 5/2 x 10 = 5/20 cm [∵ 1 cm = 10 mm]
Height of pipe = 1000 cm
Radius of vessel = 20 cm and height = 24 cm
Volume of water flow in one minute from cylindrical pipe = π (5/20)2 x 1000
= 125/2 π cm3
and volume of conical vessel = 1/3 π(20)2 x 24 = 3200π cm3
∴ Required time = (3200π x 2) / 125π
= 511/5 or 51 min 12 s
