Calculate Buoyancy of Barge: 2.8 x 10^5 kg, 19.8m Long, 10.5m Wide

[Kickbladesama]

Homework Statement

A flat-bottomed barge, loaded with coal, has a mass of 2.8 x 10 ^(5) kg. The barge is 19.8 m long and 10.5 m wide. It floats in freshwater. What is the depth of the barge below the waterline?

Homework Equations

Archimedes principle
density = mass / volume

The Attempt at a Solution

I first found the area to be 207.9 meters ^(2). Buoyant force = density x gravity x volume. I did 2.8 x 10 ^ (5) / 207.9 = 1346.80. I have no idea what to even do now. Anyone?

 

[nasu]

So you divide the mass of the barge by the area of the bottom.
Do you have any idea why have you done this?

You have the formula for the buoyant force right.
The buoyant force must be equal to the weight of the barge (it floats).
What volume of water must be displaced in order to get this force?
Once you find the volume, imagine the barge as a rectangular box. How deep must it go in the water so that the volume of the submerged part is equal to the volume found above?

 

[Kickbladesama]

I have no idea why I did it lol...