@TedShifrin I just finished the question of sketching and figuring out the volume of $\rho = \sin(\theta)$. I made it a lot harder than it had to be which brings up two questions:
1) to find the limits of integration on $\rho$, I was toiling away to try and get my function in terms of $\phi$, eventually I found no way of doing it and accepted using $\sin(\theta)$ as the upper bound. Is there a way to put it in terms of $\phi$?
2) Because I was reading fast I failed to notice that you specified bounds on $\theta$, specifically $0 \leq \theta \leq \pi$, prior to that I was stuck on trying…