Water volume sum

Question

Let's start by quoting the question.

Water flows at the rate of 10 m per minute through a cylindrical pipe of diameter 5mm. How much time would it take for it to fill a conical vessel of diameter 40 cm and depth 24 cm?

I just don't get what the question means. After doing many sums on volume, I can work it out for sure. But what has 10 m to do with a volume sum?

I'll be highly grateful to anyone who could lead me into the right track.

Answer 1

Hint:

The quantity of water that flows in a minute is $\Phi=va$ where $v$ is the rate of flow $v=1000\; cm/min$ and $a$ is the area of the section of the pipe $a=\pi r^2= 0.25 \pi \; cm^2$ .

The volume of the vessel is $V=\frac{1}{3}\pi R^2h$

can you do from this?

Answer 2

Note the rate of flow is also the height of the pipe . so calculate the volume of cone by $1/3pir^2h$. so 10 metre of water enters vessel every minute so time it would take to fill this volume is $x/10$ where $x$ is the calculated volume of conical vessel.