Let G₁ be the solid in the first octant that is inside the paraboloid 2x² + 2y² = 8 - z and below the plane z = 2. Find the volume of G₁ using iterated triple integrals in cylindrical coordinates. If f(x, y, z) = x gives the density at any point (x, y, z) in G₁, compute the mass of G₁ using iterated triple integrals in rectangular coordinates.

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