What would you like to understand?

No, $dV$ is not always equal to $dx \, dy \, dz$. In Cartesian coordinates, $dV = dx \, dy \, dz$, but in other coordinate systems, such as cylindrical or spherical coordinates, the expression for $dV$ changes to account for the geometry of the coordinate grid.

Conditions: The current setup uses rectangular/Cartesian coordinates.; In other coordinate systems, such as polar-type coordinates mentioned verbally, $dV$ may take a different form.

No, $dV$ is not always equal to $dx \, dy \, dz$. In Cartesian coordinates, $dV = dx \, dy \, dz$, but in other coordinate systems, such as cylindrical or spherical coordinates, the expression for $dV$ changes to account for the geometry of the coordinate grid.

Conditions: The current setup uses rectangular/Cartesian coordinates.; In other coordinate systems, such as polar-type coordinates mentioned verbally, $dV$ may take a different form.

$\rho(x,y,z)=xyz$ represents a variable density function where the density at any point $(x,y,z)$ inside the solid depends on all three Cartesian coordinates. It is used to set up a mass calculation for a non-uniform object.

Conditions: The object has non-uniform density.; The density is modeled as a function of position $(x,y,z)$.; This specific formula is the speaker's simplified example.

$\rho(x,y,z)=xyz$ represents a variable density function where the density at any point $(x,y,z)$ inside the solid depends on all three Cartesian coordinates. It is used to set up a mass calculation for a non-uniform object.

Conditions: The object has non-uniform density.; The density is modeled as a function of position $(x,y,z)$.; This specific formula is the speaker's simplified example.