CHALLENGE: Collecting rainwater

Question

Assume you are a high school teacher and you want to prove the following claim:
To collect rainwater using a dish "FASTER", only the area of the dish matters and its shape (being circular shape or square shape) is not important.
Unfortunately, it is not rainy. But you have a laptop equipped with your favorite programming language compiler and/or interpreter!

>>> Write a program and prove your claim!

Hint: Your students accept the fact that raindrops fall randomly.

Answer 1

With one box (×1), one box (x2) and one circle (x2) rain containers now..
https://code.sololearn.com/WHOsWK01C9yY/?ref=app

Answer 2

Here is my answer using Java.
We consider a square dish and a circular dish with the same area and let 10 million raindrops fall randomly. We count the number of the drops in each of them and compare the result. We repeat this experiment 10 times!

https://code.sololearn.com/caB71bj83Bo9

Answer 3

As you said theoritically dishes with the same area but of different shape collect the same amount of rainwater in a fixed time interval. So the challenge is to simulate an experiment to prove this fact.

Answer 4

Sorry I'm late
https://code.sololearn.com/czUa4oP5roRz/?ref=app

Answer 5

@Hamid You'r welcome! and thank you for your nice answer and your great code

Answer 6

@sayan chandea I am considering the rate (speed) of collecting rainwater. For example in an hour.

Answer 7

Yes it is the claim. And you can easily write a program to prove it. Assume you have a circular pot and a square pot whose top has the same area and compute how many random raindrops they collect in a fix amount of time

Answer 8

I'll post an answer shorly to show how to prove it using a computer program.

Answer 9

Again you have a deterministic point of view to an physical experiment. You implicitly assume the claim that I have challenged you to prove it.

Answer 10

@sayan chandra Why don't you leave the equation for a second and simulate an experiment to convince students that the equation is correct?

Answer 11

https://code.sololearn.com/WZ3aoKKud04u/?ref=app

Answer 12

Great challenge, here's my solution:

https://code.sololearn.com/clF01ZGqHG7u/?ref=app

Answer 13

My code below
https://code.sololearn.com/cEeB07Vbjfpa/?ref=app

Answer 14

This was a nice one!Thanks for the challange :-)

Answer 15

suppose r=1---circle
area is pi
suppose a is root(pi)----square
area is pi

now if i even creat a function that will take the area as parameter...
and the code will give amount..of water after sm hour

nothing will be proven...

Answer 16

see this calulates the total no. of raindrops on a dish in a particular no. of hours

https://code.sololearn.com/cfLuzIo40yS9/?ref=app

Answer 17

i dnt necessarilly find any logic of making this thing up..
equation have area in it...not shape..
so nothing to do experiment with....
if u take same two square dish...again the ratio wont be 1...ever..
if u take 1 dish fixed and other changin shape and do this 3 times answer wont be same...(1.0008 , 0.9998 , 1.004567)---((assuming they are close))
that doesnt proving anything..
cause the starting equation of calculating amount of water after a hour have area in it...

Answer 18

so its like...
there are 3 bowls suppose...(same height diff size)
so bigger the area faster the collecting...

isnt it??

Answer 19

what to prove here??
supppse its raining 50 cc/half-metre/half hour
so bigger the area bigger the collection..
random count of raindrops in an hour in both dishes are same...(not practically)-(but theoritically)

Answer 20

its a one line calculation...
like i wont even consider the dish..
just area...whatevr be the shape...
area*time*(randrops per hour per unit area)