Find the work required to empty a tank in the shape of a hemisphere of radius $\displaystyle R$ meters through an outlet at the top of the tank. The density of water is $\displaystyle p kg/m^{3}$; the acceleration of a free falling body is $\displaystyle g$. (Ignore the length of the outlet at the top.)
$\displaystyle w = \int_a^b (density)(gravity)(distance)(Area of slice)dx$
$\displaystyle w = \int_0^R (p)(g)(\pi(1 - x^{2}))(R - x)dx$