The work required to pump the water out of the spout.
The work is calculated by using the formula W=∫abf(x)dx
From the given figure, observe that the top of the given tank is rectangular in shape.
Let a rectangular slice of water at height x m from bottom have thickness =∆x m
We need to find the width of the slice at x m from bottom. Let it be w. Then by similar triangles w/x= 3/3.So the width of slice at x m height is =x m
Volume of the slice =8x ∆x m3
and weight of the slice is =(9.8×1000)(8x∆x)N.Because 1 meter cube of water has 1000 kg mass.
This slice of water must be lifted (5-x) m by the pump.
Therefore, work needed to life this slice is 9.8×10008x∆x(5-x) m J.
andtherefore, the total work required is
The work required to pump the water out of the spout is ≈1.06×106 J