In what time a cistern is filled by three pipes of diameter 2cm, 4cm a

Sir Why had we use diameter instead of radius directly in volume. Can't we calculate volume by its original formula and then put proportionate to diameter? Kindly Revert

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IMO:- E (20min)

Two ways of doing it:-

way 1

Pipe of Dia 6 cm fills cistern in 40 min

Hence in 1 min Pipe of Dia 6 cm fills (1/40) amount of cistern ------------------------1

In 1 min Pipe of Dia 2 cm fills > 2/6 * 1/40 ( as the amount of water flow is proportional to Dia)--------------------------------2

In 1 min Pipe of Dia 4 cm fills > 4/6 * 1/40 ( as the amount of water flow is proportional to Dia)----------------------------------3

Together In 1 min > adding 1+2+3

>(1/40) + 1/120 + 1/60 amount of cistern filled in 1 min
>1/20 amount in 1 min

So full Cistern in 20 min


Way 2

As per Info
Flow Amount = KD (K some constant), D= Dia of Pipe

The capacity of Cistern = T * K (D1+D2+D3) = T *K (2+4+6) = 12KT

Capacity = 6K * 40 ( as per info )
replacing in above
> 6K * 40 = 12KT
>T:- 20 min

I understand you assumed Flow rate to be proportional to D^2 (Circular Area)

Why it cant be proportional to D

given that Amount of water flowing through the pipe is proportional to the diameter of the pipe

so largest pipe ie 6cm takes 40 min so volume of tank must be 240
when all 3 pipes are opened together ; 2+4+6 ; flow rate must be 12
time taken ; 240/12 ; 20
OPTION E

Let’s calculate the cross sectional area of each pipe,
They are 1pi, 4pi and 9pi.
Thus the ratio is 1:4:9,
Total ratio 14.
Now for the bigger día. time taken is 40 mins.
So for the smaller dia. i.e., the first pipe, to complete the tank time must be 360 mins.
And for the second pipe time will be 90 mins.

Now when all are open, 1/360 + 1/90 + 1/40 = 14/360

Hence total time to fill the tank is 180/7 mins.

IMO ans is A 25 5/7 mins.

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yashikaaggarwal

Rate of the volume of water coming out of a pipe = Force at which water is flowing*Cross-sectional area of the pipe and not just one dimension

Volume is a 3 Dimensional entity which is calculated as Cross Sectional Area*Length up to which it is extended

e.g. Volume of Cube = Area of a face * Length upto which it is extended \(= a^2*a = a^3\)

e.g. Volume of Cuboid = Area of a face * Length upto which it is extended \(= (l*b)*h\)

e.g. Volume of Cylinder = Area of cross section * Length upto which it is extended \(= (πr^2)*h\)

So cross sectional area is diameter. And k is π ?

Let suppose three pipes whose diameter is
D1 = 6 ; D2 = 4 ; D3 = 2
Time taken by largest pipe , T1 = 40minutes

It is given that Water flow from the pipe is proportional to diameter
If we calculate volume of tank ,
Volume of tank = Volume of water from largest pipes = 40*6^2 * m

Volume of water by the pipe, whose diameter is 4cm = time* 4^2 * m

Volume of water by the pipe, whose diameter is 2cm = time*2^2*m

Volume of water by 3 pipes in a minute= 6^2 *m * 4^2* m * 2^2 * m
= 36m + 16m + 4m
= 56m

Total Time required by the pipes together = Volume of tank / Volume of water by 3 pipes= 40* 6^2 * m / 56* m
= 40*6*6/56
= 20*6*6/ 28
= 10*6*6/14
= 5*6*6/7
=22 5/7

Answer :A

Solution:

We are given that the amount of water flowing through the pipe is proportional to the diameter of the pipe. What it really means is the amount of water flowing through the pipe depends on the volume of the pipe. Recall that the volume of a pipe (in the shape of a cylinder) is V = πr^2 * L where r is the radius of the pipe and L is the length of the pipe. Assume all 3 pipes have the same length. We can disregard the variable L. We can also disregard the constant π. Therefore, the amount of flowing through the pipe is proportional to r^2 or to d^2 (since d = 2r). Therefore, the time, t, in minutes, taken the 4-cm diameter pipe to fill the cistern alone is:

6^2 x 40 = 4^2 x t

1440 = 16t

90 = t

Similarly, the amount of time, s, in minutes, taken the 2-cm diameter pipe to fill the cistern alone is:

6^2 x 40 = 2^2 x s

1440 = 4s

360 = s

Therefore, the combined rate of all 3 pipes is 1/360 + 1/90 + 1/40 = 1/360 + 4/360 + 9/360 = 14/360 = 7/180. Since time is the inverse of rate, the time taken for all 3 pipes to fill the cistern is 180/7 = 25 5/7 minutes.

Answer: A

Amount of water flowing is proportional to the diameter, all of you are assuming that it should be (diameter)^2 as per common knowledge of geometry while that should be clearly mentioned by the question.

sorry but this isn't correct you can't assume that the volume is proportional to the diameter square

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