Question

A remote ranch has a cylindrical water storage tank. It has a vertical central axis, a diameter of 16 ft, the sides are 5 ft high, and it is full to the brim. The depth of this water is 4 ft. How much work (in ft-lb) would be required to pump all of the water over the upper rim? (Use the fact that water weighs 62.5 lb/ft3. Round your answer to the nearest integer.)

Answer 1

Answer and Step-by-step explanation:

Given: diameter = 16ft                                                                                                                                             height = 5 ft.                                                                                                                                                                      Depth = 4ft

Work =?

As we know that work = force x distance

W= distance x density x volume                      

W= ʃ04 (5-y) 62.5x ∏ (d/2)2dy                   (area = ∏r2     ,    r= d/2)

      = 62.5 ʃ04 (5-y) ∏ (4y) dy

      =62.5∏ ʃ04 (5-y) 4ydy

        =62.5∏ ʃ04 20y-4y2dy

      =62.5∏ |20y2/2 – 4y3/3|04

      =62.5∏ |74.66|

       =14659ft.lbs (approximately)