I have found this question in the 2016 AMT maths competition and I was not able to solve it. I was wondering if any of you would be able to share some insight on how to solve this problem step by step.
It goes:
A cylindrical glass of (inside) diameter 6 cm and height 11cm is filled and then tilted to a $45\unicode{xb0}$ angle so that some water overflows. How much water is left in it?
Thank you in advance for your time. If you require further information please comment below.
Hint:
If the diameter and the height were equal, then you would drop a half of the water.