The tank is full of water and all of the water is to be pumped over the top of the tank is 643,094.07 ft-lbs .
Consider a slice shown at a height of v and suppose that the slice has a thickness of Δv. The volume of the slice is then π( 3 )^2 Δv = 9π Δv which is the area of the disk of radius 3 times the thickness of the slice.
= 62.4 ( 9 π Δ v ) = 561.6 π Δ v
Δ W = ( 561.6 π Δ v ) ( 27 − v ) = 561.6 π ( 27 − v ) Δ v ft-lbs
Work = [tex]\int\limits^{27}_0[/tex]561.6 π ( 27 − v ) d v
= 561.6 π ( 27 v − 1 / 2 v^2 ) | 27_ 0
= 561.6 π ( 27 ∗ 27 − 1 / 2 ( 27 )^2
= 1,023,516 π / 5
= 643,094.07 ft-lbs
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