A tank in the shape of an inverted right circular cone has height 12 meters and radius 13 meters. It is filled with 5 meters of hot chocolate.
Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is =1470kg/m^3

Question

A tank in the shape of an inverted right circular cone has height 12 meters and radius 13 meters. It is filled with 5 meters of hot chocolate. 
Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is =1470kg/m^3

.sam. · Answer

You could assume the entire mass of the chocolate is located at the center of mass of the cone of chocolate (which is 2/3 of the way from the bottom point = 2/3 times 5m = 3.333m above the bottom point) is raised a height of (12m - 3.333m) 8.667m.

The volume of chocolate is (1/3)B*H [both at the 5 foot level]= ( 1/3 )( 13m*5/12 )( 5m ). Multiply this by the given density and you have the mass of chocolate which has to be elevated by 8.667m.

The work is the mass x gravity x height. W=PE=mgh