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Answer:
The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j
Step-by-step explanation:
Here, we note that volume of a slice is given by
Length × Width × Height
Length of slice = Length of cylinder = 15 ft
Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then
Width of slice = 2 × √(r² - y²)
Where:
r = Radius of the cylinder =5 ft
∴ Width of slice = 2 × √(25 - y²)
∴Volume of slice = 15 ×2 × √(25 - y²)×Δy
Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy
The force required to lift the slice is the weight of the slice, which is given by
32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)
The work done by the force is the product of the force and the distsnce through which the force acts.
Work done = 40752×(10-y) × √(25 - y²)×Δy
Therefore total work done is given by
= 5094000·π J = π × 5.094 × 10⁶ j
The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j