Find the moment of inertia of the regoin bounded by z = x^2 + y^2 and z=1 if the density is propertial to the distance from the z axis
Moment of interia about the z axis = the double integral R of (x^2+y^2)*(density)dV
The Attempt at a Solution
I convert everything to cylindricals, so I get z=r^2 and z=1, but I'm not sure about setting up the integral. What exactly is region R and would the density just be == r? Anyways x^2 + y^2 = r^2, so would the integral be
integral of r^2 * r * r * dθ dr, 0≤θ≤2π, 0≤r≤1
Basically im just unsure what region R is, right now the limits are just the area bounded by the plane and parabloid but what about the volume underneath? Also why do the moments of inertia about the x and y axis involve triple integrals and z doesn't or are my notes wrong? Any help is appreciated.