To find the total mass of water, \(M\), we proceed in an analogous way, and determine the value of the sum (integral) of all of the mass elements: \[\begin{aligned} M = \int dm = \int_0^h \rho \pi a^2...To find the total mass of water, \(M\), we proceed in an analogous way, and determine the value of the sum (integral) of all of the mass elements: \[\begin{aligned} M = \int dm = \int_0^h \rho \pi a^2 z dz = \rho \pi a^2 \left[ \frac{1}{2}z^2 \right]_0^h= \frac{1}{2}\rho \pi a^2 h^2\end{aligned}\] Substituting this value for \(M\), we can determine the \(z\) coordinate of the center of mass of the full bowl: \[\begin{aligned} z_{CM} &=\frac{\rho \pi a^2}{3M}h^3 = \frac{2\rho \pi a^2}{3\rho \pi …
