A cone with height 12 ft and radius 6 ft, pointing downward, is filled with water to a depth of 3 ft. The density of water is 62.4 lb/ ft3.

(a) Consider a slice of water that is Δh ft thick and located h ft from the bottom of the cone. Write an expression giving the work required to pump the slice out over the top. Give your answer using the form below.
Density · Volume of slice · Displacement of slice
Density =

lbs/ ft3

Volume of slice =

ft3

Displacement of slice =

ft

(b) Use an integral to find the exact work required to pump all the water out over the top.

Question

A cone with height 12 ft and radius 6 ft, pointing downward, is filled with water to a depth of 3 ft. The density of water is 62.4 lb/ ft3.

(a) Consider a slice of water that is Δh ft thick and located h ft from the bottom of the cone. Write an expression giving the work required to pump the slice out over the top. Give your answer using the form below.
Density · Volume of slice · Displacement of slice
Density =   

 lbs/ ft3

Volume of slice =   

 ft3

Displacement of slice =   

 ft

(b) Use an integral to find the exact work required to pump all the water out over the top.