Need ASAP- How much work will it take to pump the liquid

Question

A container of radius 8 ft and height of 32 ft is filled to a height of 27ft with a liquid weighing 51.8 lb/ft² .How much work will it take to pump the liquid to a level of 5 ft above the cone's rim?

Answer 1

Assuming an inverted cone.

The simplest way to do this is to concentrate all the weight of the liquid at a point at the center of gravity of the liquid. Then compute the work to move the distance from the center of gravity to 5 feet above the tank.

Center of gravity of cone shaped liquid = (3/4)height = 20.25 ft

Distance = distance from cg to top of tank plus 5 feet = (32-20.25) + 5 = 16.75 feet

Weight = ρ × Volume of cone = ρπr²h/3

Work = Weight × Distance = (51.8)π8²(27)/3 × 16.75 ft-lbs