1. The problem statement, all variables and given/known data A vase is filled to the top with water of uniform density f = 1. The side profile of the barrel is given by the surface of revolution obtained by revolving the graph of g(z) = 2 + cos(z) over the z-axis, and bounded by 0 ≤ z ≤ π. Find the mass of the vase. 2. Relevant equations 3. The attempt at a solution So I know that Mass = the triple integral of density dV. I need to find my bounds. I would like to use spherical coordinates as it seems to make sense with this problem. Theta goes from 0 to 2pi. phi goes from 0 to pi ? since it is bounded by 0 and pi? Or am I wrong here? and rho goes from 0 to something involving the g(z) equation, but I am not sure how to manipulate it :/. Any tips to get me started or confirmation on the phi bounds would be great.