Question

Water flows through a circular pipe of radius 7cm at the rate of 5m/sec into a reservoir in the
shape of a cone surmounted by a cylinder If the common diameter be 7m and heights of
conical and cylindrical parts are 12m and 11m respectively, find the time taken to fill the
reservoir

Answer 1

Answer:

The volume of water that flows through circular pipe per second is equal to the volume of the pipe.

Volume of circular pipe  = π r² h,

where r is the radius of the pipe and h is the distance traveled by the water in the pipe.

Therefore, volume of the pipe  = π (7/100)² * 5

We know that π = 22/7

Therefore, volume  = 0.077 m³ ............................. (1)

Now, the volume of the reservoir = Volume of cone + volume of cylinder

or, Volume of reservoir = 1/3 π r² h + π R² h

= 1/3 π (7/2)² *12 + π (7/2)² * 11

= π (49/4) [ 4 + 11]

= π (49/4) * 15

= 577.5 m³ ............................................. (2)

Time taken to fill the reservoir = Total volume of the reservoir/ Volume of pipe

= 577.5/ 0.077

= 7500 seconds

= 125 minutes

= 2.08 hours

So ,the answer is 7500 seconds or 125 minutes or 2.08 hours.