Find the force on a hollow dome that is 1000 feet in diameter, that is a mile below the surface. HOw large can the dome be expanded and not surpass 600 billion pounds.

Question

I know the height will be 500, and i think that the intergral is 5280 to 4780 int 64,000pih, I am not sure thoug. any help would be much appreciated.

Answer 1

Is this in water on earth?
Do you mean the buoyant force (the net force of water on the sphere)?
If so, use Archimedes principle. The force up is equal to the weight of water displaced.
= rho g (4/3) pi r^3