Like problem 8-55, the rotating radius will be horizontal (because the axis of rotation is vertical). Consequently, the bounds of integration will be y-values: from $y = 1$ to $y = 13$. Both the bounds and the integrand will be written in terms of $y$.

Unlike problem 8-55, there will be a cylindrical hole in the center of this 3D figure. This hole has a radius of $1$.

Unlike problem 8-55, the outer function is no longer $f\left(y\right)$. It is $1$ unit longer than $f\left(y\right)$.