Answer
The volume of fresh water displaced is $~~0.33~m^3~~$ more than the volume of salt water displaced.
Work Step by Step
The boat displaces its weight in water.
Since the weight of the fresh water displaced by the boat is $35.6~kN$, the weight of the boat is $35.6~kN$
Therefore, the weight of the salt water displaced by the boat is $~~35.6~kN$
We can find the volume of the fresh water that is displaced:
$V = \frac{mass}{\rho}$
$V = \frac{weight}{g~\rho}$
$V = \frac{35,600~N}{(9.8~m/s^2)(1000~kg/m^3)}$
$V = 3.63~m^3$
We can find the volume of the salt water that is displaced:
$V = \frac{mass}{\rho}$
$V = \frac{weight}{g~\rho}$
$V = \frac{35,600~N}{(9.8~m/s^2)(1100~kg/m^3)}$
$V = 3.30~m^3$
We can find the difference:
$\Delta V = 3.63~m^3-3.30~m^3 = 0.33~m^3$
The volume of fresh water displaced is $~~0.33~m^3~~$ more than the volume of salt water displaced.
