Find the Moment of Inertia About The $z$ -Axis of a Thin Funnel in the Shape of a a Thin

Short Answer

Find the moment of inertia about the $z$ -axis of a thin funnel in the shape of a cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } } , 1 \leq z \leq 4$ , if its density function is $\rho ( x , y , z ) = 14 - z$ .