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- How to calculate the air pressure of captured air under water with a weight pushing it downwards

For a construction I am building, I am stumbling on a rather basic physics question regarding pressure.

Let's say I have a cubic bucket of 1m^3 that I place upside down on a water surface. I add a downward force (weight) of say 1000N submerging the bucket under water with the air captured inside.

What is the pressure and volume of the air inside the bucket? My own attempt:

The buoyancy force is also 1000N and is spread over the 1m2 surface, so the pressure is increased with 1000N/1m2 =~ 0.01 atm. Thus the resulting pressure is 1.01 atm, the volume is 1m3 / 1.01 and the waterline inside the bucket would be 1cm above the edge of the bucket.

My confusion is that this would mean that a bucket of the same volume but a smaller width/height would result in higher pressure of the air inside which seems counterintuitative.

Can someone help?

Let's say I have a cubic bucket of 1m^3 that I place upside down on a water surface. I add a downward force (weight) of say 1000N submerging the bucket under water with the air captured inside.

What is the pressure and volume of the air inside the bucket? My own attempt:

The buoyancy force is also 1000N and is spread over the 1m2 surface, so the pressure is increased with 1000N/1m2 =~ 0.01 atm. Thus the resulting pressure is 1.01 atm, the volume is 1m3 / 1.01 and the waterline inside the bucket would be 1cm above the edge of the bucket.

My confusion is that this would mean that a bucket of the same volume but a smaller width/height would result in higher pressure of the air inside which seems counterintuitative.

Can someone help?