If the pot can contain twice as many in volume, is it twice as heavy? Suppose that I have two pots that look like similar cylinders (e.g. Mason jars). I know that one of them can contain twice as many in volume than the other. If both are empty, is the bigger one twice as heavy as the other?
Intuitively I would say that it is less than twice as heavy, but I am not sure. Mathematically, I do a cross multiplication and conclude that the bigger one is twice as heavy, but it seems wrong to me. How to solve this problem?
Note: This is for an actual real life problem. I filled up the bigger pot and sealed it but I forgot to weigh it before and now I want to know how many grams of food it contains.
EDIT: The width of the walls seem to be the same. Can we find what is the weigh of the bigger one given the weigh of the smaller one?
 A: If it is important, you really need to get sample empty jars and weigh them. I have some jars by an American company, one is pint size, the other quart. Both say "wide mouth" and take exactly the same size lid. Also, I cannot tell for sure whether the glass is the same thickness in both. That is the most important question here, is the glass the same width or a little thicker in the bigger jar? Looking at them, the jars are also not perfectly proportional. 
If the glass is the same thickness, the larger one should be about $$ 2^{2/3} \approx 1.587 $$ times as heavy. We do not really know.
A: Your intuition is right. It is in fact roughly
$$2^{2/3}=1.5874...$$
times as heavy. So less than twice as heavy.
This comes from the fact that the volume of a solid is proportional to the cube of the lengths, and the surface is proportional to the square of the lengths.
A: No, it is not twice as heavy. The weight of the pot is determined by its mass, which is proportionate to its surface, rather than its volume.
A: If the walls have the same width, then the mass is proportional to the surface of the walls. 
A similitude of magnitude $2$ in volume gets the surfaces larger by a factor $\sqrt[3]{4}$, so the mass is $\sqrt[3]{4}=1.587..$ times the one of the smaller pot
A: If the pots are made of the same thickness of metal, then no.
Let $r$ be the radius, and $h$ be the height.
Let's say the pots have the same shape, so $r/h = C,$ some constant.
The weight of the pot is then proportional to the outer surface area:
$$ A = \pi r^2 + (2 \pi r^2 / C) = \pi r^2\left(1 + \frac{2}{C}\right).$$
But the volume is
$$V = \frac{\pi r^3}{C}.$$
Therefore, a pot that holds double the volume has an $r$ that is $\sqrt[3]{2}$ times that of the smaller.  But the weight, then, is $\sqrt[3]{4}$ times that of the smaller one, not double.
Of course, all bets are off if anything is different about the thickness of the pot, the form factor, etc., so it's better just to weigh then both.
