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Calculus/Calculus - Related Rates word problem

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Expert: Scotto - 7/21/2008


Question
Hello!  

I'm having trouble picturing a word problem and thus having trouble discerning what the appropriate formula for its area should be.  The problem reads:  "A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 12 ft3/min, how fast is the water level rising when the water is 6 inches deep?"

I've read on a few answer boards that I'm to use the formula 1/2blw to get the area of the trough but I can't see how that would be...could you please explain this to me?  Thank you very much in advance!

Stu

Answer
The width is 3 at the top and 0 at the bottom.  The have a height of 1 foot.  Using these two pieces of information, the width of the water is 3x where x is the depth that has been filled.  The trough is 10 feet long, and that's constant.

The surface area when the water is 6 inches deep (0.5 feet) is then 10*0.5*3 = 15.  Water is flowing in is at 12 ft^3/min.

The change in depth is then 12/15=0.8 ft/min.

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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