# Archimedes' principle -- Which box will sink first as we add coins....

• dkk
In summary, the problem is about determining which of the given box sizes (p x l x t) can hold the most coins before sinking, assuming they are all filled with coins one at a time and do not tilt. The key factor is the volume of the box above the water level, which means that the box with the largest volume (8 x 8 x 4 cm3) should be able to hold the most coins. This is because it will displace the most water, allowing it to float better than the other boxes.f

#### dkk

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There are five empty box contains with the same weight. The upper side of each boxes are removed. These boxes are floating in a pool of water. Then to each box we put coins slowly one by one. Assuming the box does not tilt. Determine which of the following size of the box (p x l x t) can be filled with most coins before it sinks.

A.) 4 x 4 x 11 cm3
B.) 6 x 6 x 6 cm3
C.) 8 x 8 x 4 cm3
D.) 10 x 10 x 2 cm3
E.) 12 x 12 x 1 cm3

Don't have the answer, but I chose C as the answer. All boxes have the same weight. The box with the larger volume should be able to float better than the other boxes right?

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Right.

I think it might be a little more complicated than that. Imagen that you add the same amount of coins to all the boxes at once and they all are sinking down. What do you think will happen?

I think it might be a little more complicated than that. Imagen that you add the same amount of coins to all the boxes at once and they all are sinking down. What do you think will happen?
First off you are changing the problem that says that the coins are added one at a time. However, I will imagine (as you asked me to do) that the same amount of coins are added to all boxes and that they all sink down. What I think will happen (as you said) is that they will all sink down. The point of the problem as stated is that the box that displaces the most water will hold the highest number of coins. Your point is ... ?

I was just engaging with the problem throught a thought experiment and wondering what will be the difference between long slim boxes and fat low boxes as they sink while they hold the same amount of coins in order to get a better feeling for the problem, but you are right because the volume above the water level actually holds the answer to this problem.