A cone with height 8 ft and radius 6 ft, pointing downward, is filled with water to a depth of 2 ft. All of the water will be pumped out over the top of the cone. The density of water is 62.4 lb/ ft ³  .

(a) Consider a slice of water that is Δh ft thick and located h  ft from the bottom of the cone. Use Delta or the CalcPad for Δ. Leave π in your answer.

Volume of slice = π(3h/4) ²  Δh 

Displacement of slice =   ???? ft 

(b) Find the endpoints of the integral needed to find the exact work required to pump all the water out over the top.

Lower endpoint = 0

Upper endpoint =  ?????