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

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

    A trough is 9 feet long and foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of from to . 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 View Post
    A trough is 9 feet long and foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of from to . 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.....
    attached graph is an end view of the trough ...

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

    W = 62 \int_0^1 \left(18y^{1/4}\right) \cdot (1-y) \, dy
    Attached Thumbnails Attached Thumbnails Work problem- pump water but not sure the size of the tank?-quarticcrosssection.jpg  
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