Answer
The average density of the fish is $1081~kg/m^3$
Work Step by Step
We can find the mass of the fish:
$mg = 200.0~N$
$m = \frac{200.0~N}{g}$
$m = \frac{200.0~N}{9.80~m/s^2}$
$m = 20.408~kg$
We can find the buoyant force exerted on the fish:
$F_b = 200.0~N - 15.0~~N = 185.0~N$
According to Archimedes' principle, the buoyant force is equal to the weight of the water that is displaced. We can find the volume of the water that is displaced. Note that this volume is also the volume of the fish:
$mg = F_b$
$\rho_w~V~g = F_b$
$V = \frac{F_b}{\rho_w~g}$
$V = \frac{185.0~N}{(1000~kg/m^3)(9.80~m/s^2)}$
$V = 0.01888~m^3$
We can find the density of the fish:
$\rho = \frac{m}{V} = \frac{20.408~kg}{0.01888~m^3} = 1081~kg/m^3$
The average density of the fish is $1081~kg/m^3$
