Answer
The average density of the goose is $250~kg/m^3$
Work Step by Step
If the goose is floating on water, then the buoyant force is equal in magnitude to the weight of the goose. According to Archimedes' principle, the buoyant force is equal to the weight of the water that is displaced.
Let $V$ be the volume of the goose. Let $m_c$ be the mass of the goose. Let $m_w$ be the mass of the water that is displaced by the goose.
We can find the average density $\rho_c$ of the goose:
$m_c~g = m_w~g$
$\rho_c~V~g = \rho_w~(0.25~V)~g$
$\rho_c = 0.25~\rho_w$
$\rho_c = (0.25)~(10^3~kg/m^3)$
$\rho_c = 250~kg/m^3$
The average density of the goose is $250~kg/m^3$.
