Define a solid region E as
E = \{(x, y, z) \mid 1 \le x^2 + y^2 \le 4, \ -y - 2 \le z \le y^2\},
where x, y and z are measured in meters.
(i) Sketch the projections of the region E onto the xy-plane and the yz-plane.
(ii) Set up a triple integral in cylindrical coordinates that gives the volume of solid
E. Do not evaluate the integral.
(iii) Given that the density of solid E varies according to \(\rho(x,y)\) below, set up and
evaluate a triple integral that gives the mass of solid E.
$\rho(x, y) = \frac{1}{x^2 + y^2}$ \((kg/m^3)\)
