Finding volume with triple integral, how do i do this?

Cylindrical coordinates seems like the way to go. To find the intersection, solve the equations simultaneously. The easiest way to start doing this is by squaring the half cone equation to get z^2 = x^2 + y^2. Then, since the other equation is z = x^2 + y^2 you must have z^2 = z. From this you can easily solve for z, and then the x and y ...