The question relates to the energy required to pump water out of the
spout at the top of the triangular prism tank.
The width of the layer of water Δx thick is x m.
Reasons:
The location of the layer Δx m thick = x meters above the bottom
The length of the triangular (cross-section) prism tank = 8 meters
The length of the layer Δx thick layer = 8 meters
From the attached drawing of the cross-section of the tank, we have;
The height of the triangular tank cross-section = 3 meters
The length of the base of the triangular cross-section = 3 meters
By similar triangles, we have;
[tex]\dfrac{Height \ of \ Tank}{Base \ length \ of \ tank}= \dfrac{Height \ of \ layer \ with \ thickness \ \Delta x }{Width \ of \ layer \ with \ thickness \ \Delta x}[/tex]
Which gives;
[tex]\dfrac{3}{3} =\dfrac{x}{Required \ width}[/tex]
[tex]\dfrac{3}{3} =1 = \dfrac{x}{Required \ width}[/tex]
Required width × 1 = x
The required width = x m
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