Work problem- pump water but not sure the size of the tank?

A trough is 9 feet long and http://math.webwork.rochester.edu:80...6774a851b1.png foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of http://math.webwork.rochester.edu:80...7b715f83d1.png from http://math.webwork.rochester.edu:80...23640869f1.png to http://math.webwork.rochester.edu:80...9a70c4f3b1.png. The trough is full of water. Find the amount of work required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.

I understand how to do these problems in general but how can you find the volume if not given the width?I guess I don't understand what "vertical cross-section of the trough parallel to an end" means.....

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Re: Work problem- pump water but not sure the size of the tank?

Quote:

Originally Posted by

**makeupgirl1107**

attached graph is an end view of the trough ...

a representative "horizontal slice" of water has length $\displaystyle 9$ ft, width $\displaystyle 2y^{1/4}$ ft , and thickness $\displaystyle dy$ ft.

$\displaystyle W = 62 \int_0^1 \left(18y^{1/4}\right) \cdot (1-y) \, dy$