Question

Water flows at the rate of 15m per minute through a cylindrical pipe, having the diameter 20mm. How much time will it take to fill a conical vessel of base diameter 40cm and depth 45cm?

Answer 1

Answer:

Speed of flowing water from pipe

= 15m/min = 1500cm/60sec = 25cm/sec

Speed of flowing water = 25cm/sec

We have diameter of pipe=20mm

So radius of pipe, r =10mm = 1 cm

Let length of pipe be, h =?

We have given parameters of cone,

Diameter=40cm

So, radius,R =20cm

And

Height of cone , H = 45cm

We have to fill the cone by the water flowing through the pipe in a considerate time

Therefore, volume of cylindrical pipe will be equal to the volume of cone

1/3×22/7×R^2×H = 22/7× r^2×h

(22/7 will be eliminated being on both sides of equal sign)

So,

Putting values:

1/3×20×20×45 = 1×1×h

{Since ( length of pipe is unknown)}

h=6000cm

It means length of pipe is 6000cm and speed of water flowing is 25cm/sec

We have to find the time in which water will travel 6000cm in the given speed

We know, speed = distance / time

So, time = distance / speed

Hence,

Time taken to fill the

conical vessel = 6000/25

= 240 sec

So, time taken = 4 minutes = 240 seconds.