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Question

A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has height 50cm. If the trough is being filled with water at a rate of .2m³/min, how fast is the water level rising when the water is 30cm deep?

Answer 1

Hi Suyong P.,

Did you draw a sketch of the trough, in cross-section? That should convince you that when the water is 30 cm deep out of 50 cm trough height, the waterline width is 60% of the change from 30 cm to 80 cm -- in short, 60 cm. You are thus filling an area of (60 cm x 10 m) at a rate of 0.2 m^3 min^(-1). Suggest division is the operation you need? Always carry your dimensional units over through a calculation, to make sure that you did the right calculation!

-- Cheers, --Mr. d.

P.S. Hope you don't come up dry on this one, that would suggest a misreading of the problem ....