Question

When a load of 1(10)^6 N is placed on a ship, the ship only sinks 2.5 cm into the ocean (sea water). Estimate the cross-sectional area of the ship at water level.

Answer 1

How amusing - you happened upon a Naval Architect.

increased volume of ship in the water = Area * .025 meters

mass of water displaced = density of seawater * that volume

density of seawater is about 1029 kg/m^3

so
mass of water displaced = 1029 * .025 * A

Buoyancy force due to that water = mass * 9.81 m/s^2 gravity

so
additional buoyant force up
= 9.81*1029 * .025 * A

so Archimedes says
1,000,000 = 9.81 * 1029 * .025 * A