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 | 28th Feb, 2011, 07:02: PM

Expert Answer:

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.
begin mathsize 16px style 1 third cross times 22 over 7 cross times fraction numerator begin display style 21 end style over denominator 2 end fraction cross times 21 over 2 cross times 12 equals 22 over 7 cross times 7 over 200 cross times 7 over 200 cross times 5 straight x
rightwards double arrow straight x equals 72000 space min
rightwards double arrow straight x equals 72000 over 60 equals 1200 space hr end style
 
We hope that clarifies your query.
 
Regards,
Team
TopperLearning

Answered by  | 30th Nov, 2017, 02:34: PM