How much deeper does the barge lower?

[keithcuda]

Homework Statement

1. A rectangular barge floats in freshwater. When a 400 kg block is loaded on the 5 m long by 2 m wide barge, the barge sinks a few centimeters deeper. How much deeper does the barge lower?

Homework Equations

Archimedes' principle
This is where I am stuck. My textbook doesn't talk much about this at all.

The Attempt at a Solution

 

[Bystander]

You've done all the hard work. How much deeper does the barge have to "sink" to displace the extra 0.4 m³?

 

[keithcuda]

You've done all the hard work. How much deeper does the barge have to "sink" to displace the extra 0.4 m³?

 

[haruspex]

View attachment 78234

Yes, but you could have got there a bit faster from knowing the volume displaced and the area.