Damn, 123% rise.
mm sugar water
Quick ‘proof’ the taller the can, the more material used:
Consider two cases ignoring the top and bottom only focussing on the surface area. In the first case, you flatten so much the can has no height. This forms a ring that when unwrapped makes a length of 2 pi R.
Now stretch the can to be ‘infinitely’ long. By construction, this is longer than 2 pi r. Given both are made of aluminum, and have the same density, the larger can has more mass requiring more material.
The total mass must be a continuous function ranging from the linear mass density times the circumference of the circle to the same mass density time times the ‘length’ of the infinite line. This must remain true for any small increase in length between the two.
I’ll leave this as an exercise to the reader. What if the circle has an infinite radius?
The fuck is a fluid ounce?
This cannot be a real question.
surely this uses more aluminum
I’m shit at math, but probably not? If both contain the same amount of liquid, are filled to the same point and both are round (which they are lol), I don’t see how those would require more material.
And even if, if they double the price per can, it’s absolutely worth it.
You have never taken calculus.
