Answer
$I_z=2 \pi a^3 \delta$
Work Step by Step
As we are given that $x^2+y^2=a^2$
and $I_z=\int_C (x^2+y^2) \delta ds$
or, $I_z=\int_C (a^2) \delta ds$
or, $I_z=a^2 \delta \int_C ds$
We know that $\int_C ds =2 \pi a$, the circumference of the curve
Then $I_z=2 \pi a^3 \delta$
