Question

A rectangle trough is 8 meters long, 2 meters across at the top, and 4 meters deep. If water flows in at the rate of 2 cubic meters per minute, how fast is the surface rising when the water is 1 meter deep?

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Answer 1

"rectangle trough". What does the cross section look like? is the cross section a triangle, or a truncated triangle?

Answer 2

I assume a triangular cross-section. So, the width of the water surface when it has a depth of y is y/2. Thus the volume of water of depth y is

v = (1/2)(y)(y/2)(8) = 2y^2
dv/dt = 4y dy/dt

Now just plug in your numbers