A sailboat sank to the bottom of a lake. The majority of the boat's mass is from the 0.25m^3 of lead in its keel. The density of lead is approximately 11,000 kg/m^3. The density of water is approximately 1000 kg/m^3. Because gravity is pretty much the same everywhere on earth, the weight of the sailboat can be assumed to be approximately equal to its mass.
In kilograms, what total weight of water needs to be displaced in order to lift the sailboat to the surface?

In order for the sailboat to be lifted and float at the surface of the water, the upward force of buoyancy must be equal to the downward force of gravity on the boat.

According to Archimede's principle in fact, the upward buoyant force that is exerted on a body in a fluid is equal to the weight of the fluid displaced by the body.

So we can write:

[tex]B=F_g[/tex]

where

B is the force of buoyancy, which is equal to the weight of the water that must be displaced in order to lift the sailboat

[tex]F_g=\rho V g[/tex] is the weight of the boat, where

[tex]\rho=11,000 kg/m^3[/tex] is the density of lead

[tex]V=0.25 m^3[/tex] is the volume of the boat

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

Substituting,

[tex]B=(11,000)(0.25)(9.8)=26,950 kg[/tex]