Answer
$I_y=365in^4$
Work Step by Step
We can find the required moment of inertia as follows:
$I_y=\Sigma (I+Ad^2_x)$
We plug in the known values to obtain:
$I_y=\frac{10(6)^3}{12}+\frac{6(10)}{2}(3)^2-\frac{6(3)^3}{36}+\frac{(6)(3)}{2}(5)^2-(\frac{\pi (2)^4}{4}+(2)^2\pi (3)^2)$
This simplifies to:
$I_y=365in^4$
