#### To determine

**To find:**

The work required to pump the water out of the spout.

#### Answer

1.06×106 J

#### Explanation

**1) Concept:**

The work is calculated by using the formula W=∫abf(x)dx

And weight=gravity·volume

**2) Given:**

**3) Calculation:**

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

W=∫abf(x)dx

W≈∫039.8×1035-x8xdx

=9.8×103∫0340x-8x2dx

=9.8×10320x2-83x303

=9.8×1032032-8333

=9.8×103180 -72

=9.8×103108

=1058.4×103 J

=1.06×106 J

**Conclusion:**

The work required to pump the water out of the spout is ≈1.06×106 J