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

• Apr 11th 2012, 04:55 PM
makeupgirl1107
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.....
• Apr 11th 2012, 05:36 PM
skeeter
Re: Work problem- pump water but not sure the size of the tank?
Quote:

Originally Posted by makeupgirl1107
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.....

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.

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