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Instantaneous Rate of Change of Water

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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 ft^3/min, how fast is the water level rising when the water is 6 inches deep?

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Solution Summary

This uses the water level in a trough to show how ot determine instantaneous rate of change.

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If you draw a careful picture of the trough, you will realise that it is basically a prism with its top open (where it is being filled!). The volume of a prism is V = Area of Cross-Section x Length.

The Area of Cross Section is the area of any one of the ...

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