A cone-shaped water reservoir is 20 ft. in diameter and 20 ft. deep. If the reservoir is filled to a depth of 10ft., then write the integral which represents the amount of work required to pump all the water to the TOP of the reservoir.

Answer 1

The work required is proportional to the height, measured from the bottom.

This integral is S (pi*R(H)^2)*(density)*g H dH. S denotes the integral sign

The cone radius as a function of height is R(H) = H/2

Integrate from H = 0 to h = 20 ft

In these British units, (density* g = 62.4 lb/ft^3. The answer will be in ft-lb