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(r² + y²)z², where A is a constant. (a) Show that the density expressed in spherical coordinates (r, 0,0) is p= Ar (1- cos? 0) cos? 0. (b) Hence, or otherwise, find the mass of the shell by evaluating a suitable volume integral. Hint: You may find the substitution u= cos 0 useful.

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