1. The problem statement, all variables and given/known data So we have a glass consisting of a 10 cm long cylinder on top of a 1 cm long bottom standing on a table. The radius is 3 cm. For every x in [0, 10] we let h(x) be the height of the center of mass when we fill the glass with x cm water. That is, h(x) is the distance from the table to the center of mass. We have h(x) = (m_b*h_b + m_c*h_c + m_w*h_w) / (m_b + m_c + m_w), with m_b = mass of bottom = 10 gram h_b = height of center of mass in bottom = 0.5 cm m_c = mass of cylinder = 50 gram h_c = height of center of mass in cylinder = 6 cm m_w = mass of water = 9*pi*x h_w = height of center of mass in the water = 1 + x/2 cm Now the task is to find where h(x) decreases and increases for x in [0, 10]. Which height of water gives the lowest center of mass in the glass, and what is h(x) for that x-value? 2. Relevant equations 3. The attempt at a solution By differentiating h(x) I found that x = 2.550553126 makes h(x) be the lowest. h(2.550553126) = 3.550553126. This puzzled me. Why is the center of mass exactly 1 cm over the water level when h(x) is at its lowest? Does someone have a mathematical or physical explanation to this?