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# Pouring Problem

##### Age 7 to 11 Challenge Level:
Harvey from Hanley Swan Primary wrote:

I thought that it would probably overflow because it didn't look like the water in the first cup could fit in the second as they were the same size. I watched the video and was very surprised about what happened. AMAZING! I think that the reason it managed to fit is that there was a bit of a widening in the top of the cup - the water in the first cup didn't reach this point.

Mimi from Primrose Hill said:

The twist is that both glasses are filled up high and she poured it without the water overflowing. What may be the solution (I am not so sure...) is that the bit in the cup where it grows out near the top, makes the water fill up less (by which I mean it stores more water) and so that makes it stay at the top. Another reason could be that part of the water in the second glass is fake. Therefore, if my reasons are wrong I will not be very surprised.

Nathan from Canberra Grammar School in Australia sent this:

The two glasses Maya has used have an opposite bottleneck. So the volume of the very top of the glass is larger than the volume of the bottom of the glass.

Amy from Luckwell Primary School gave a very clear explanation of what she thinks happened:

Like most people who watched this video, I predicted that the glass which the water was being poured into would overflow. I was a little suspicious, though, as the question 'Were you surprised?' usually means that something unexpected will happen...
What is happening is we are confusing our eyes and assuming that the top half of the glass is smaller than the bottom half. Yes, the top half of the glass is shorter, but it's also wider! On top of this, the bottom half is thinner and we do not pay attention to the shape of the glass as we're
watching Maya pour the water into the right-hand glass. (From now on, pay attention to the shape of your glass!).
When I showed my friends the clips, they were amazed! I was the only one that figured out how it happened though...

Maths Mayhem at North London Collegiate School wrote:

We watched the video as a maths club and were surprised by what happened as we thought it would overflow if you kept pouring.
Kayla thought because the glass is narrower at the bottom and wider at the top, the amount of water in the left-hand glass is the same volume as the space left in the right-hand glass.
Isha thought that both cups were more than half full when she first saw them but now concludes that they have to be half full to start.
We all then speculated that the right-hand glass is slightly wider and taller than the other and maybe the base is slightly larger, however, we couldn’t say for sure as we don’t have it to measure.
In conclusion, we have decided that because of the shape of the glasses that this is an illusion. The glasses look more than half full but they are only actually half full.

Here's a very different solution from Abdullah who is homeschooled:

I think, in the right glass there is water and that in the left glass there is alcohol.
Because the alcohol particles are smaller than water particles, the alcohol particles go into spaces, which are between the water particles.
When we studied the States of Matter, we did an experiment:
First, we put 10 ml water in a measuring cylinder. And we put 10 ml ethanol in another measuring cylinder. And then we added 10 ml ethanol on the 10 ml water. The reading was 18 ml.