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water flows at the rate of 5m per minute through a cylindrical pipe whose diameter is 7cm. how long it will take to fill the conical vessel having base diameter 21 m and depth 12 m.
Asked by deep_72 | 28 Feb, 2011, 07:02: PM
Dear student,

We have:
r = radius of the base of the conical vessel = 21/2 m
h =height of the conical vessel = 12 m
So, volume of the conical vessel =  1/3 × 22/7 × 21/2 × 21/2 × 12... (1)
Suppose the conical vessel is filled in x minutes.
Then, length if the water coloumn = 5x m

Clearly, water column forms a cylinder of length 5x m, and radius 7/ 2 cm = 7/ 200 m
So, volume of water that flows in x minutes is given by:
22/7 × 7/200 × 7/200 × 5x.....(2)

Equate equations (1) and (2) to get the required value of x.

We hope that clarifies your query.

Regards,
Team
TopperLearning
Answered by | 30 Nov, 2017, 02:34: PM

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