A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on the origin. The shell is made of a material with density p = A(x2 + y2) z2, where A is a constant.  Show that the density expressed in spherical coordinates (r, θ, φ) is p = Ar4(1 − cos2 θ) cos2 θ.

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