Can anyone please explain how this maths problem works?

Question

The volume of the pool is 1512 m squared, the volume of the cylinder is 6872 cm cubed. When the pool is emptied, the water flows through a cylindrical pipe of radius 12.5 cm.

The water flows along this pipe at a rate of 14 centimetres per second.

Calculate the time taken to empty the pool.

Give your answer in days and hours, correct to the nearest hour.

The answer is (1512/6872 * 1000000) / (60 * 60 * 24) = 2 days 13 hours

Answer 1

Volume = 1512m CUBED(yes?).The volume out of the pool per second is cross sectional area of pipe(Pi*r^2) times speed of flow per second;which gives Pi x (14.5) * 2 x 14 = 9247 cubic cm per second.There are 100 x 100 x 100 cubic cm in a cubic m=1000,000.So the water flows out at 9247/1000000 cubic metres each second.I think you should be able to solve from here on.Good luck.

Answer 2

First we have to find out how many m cubed of water go through the pipe for 1 second. This is actually the volume of a cylinder of radius 12.5 cm and height 14 cm, which, as you have calculated, is 6872 cm cubed. However, we need this in m cubed because the volume of the pool is given in m cubed.

1 cm = 0.01 m, so 1cm cubed = 1 cm * 1cm * 1cm = 0.01 m *0.01 m * 0.01 m = 0.000001 m cubed = 1/1000000 m cubed

So, 6872 cm cubed = 6872/ 1000000 m cubed

Now, we know that the pool loses 6872 / 1000000 m cubed water per second.

But time taken = done work / speed of working

Here the work is the quantity of water drawn from the pool and the speed of working is the rate at which we draw water

so, time taken = 1512 m cubed / (6872/1000000) m cubed/second =

= (1512 / 6872) * 1000000 seconds

however, we need our answer in days and hours and not in second, so we have to see how many seconds there are in one day

1 day = 24 hours = 24* 60 minutes = 24*60*60 seconds

so 1 second = 1day / (24*60*60)

That is why the final answer is

((1512/6872) * 1000000) / (60 * 60 * 24) days

Hope this helps :)

Answer 3

I will assume you meant to say that the volume of the pool is 1512 m^3. Is that right?

Water outflow rate through the pipe is:

outflow = O = A*rate = pi(12.5^2)14 cm^3/sec

O = 6872 cm^3/sec

O = 6.872x10^-3 m^3/sec

time = 1512/ 6.872x10^-3 seconds

time = 2.2x10^5 seconds

time = 2.2x10^5/3600 hours = 61.11 hours = 2.5462 days

time = 2 days 13 hours and a few minutes