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Calculus/related rates

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Expert: - 11/8/2009


Question

trough
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.



(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.5 feet deep? (Round to three decimal places.)

1 ft/min



(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.5 ft, determine the rate at which water is being pumped into the trough. (Round to three decimal places.)  

Answer
(a) To do this, we need to know the surface area.
Since width = height, to width a the surface is 1.5' as well.
To find the surface area, take 12(1.5) = 18.

Since the water is coming in at 2 cubic feet per minute,
the rise at that point is 2/18 = (1/9)'/min.

(b) When h = 2.5, width of the water on top is also 2.5.
Since the length is 12, the area at this point is 12(2.5) = 30.
If we take 30(3/8), we get 90/8 = 45/4 = 11 1/4 ft³/min.

Scotto

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