Calculus

A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 10 cm deep?
Round your answer to 3 decimal digits.

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  1. see related questions below.

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  2. After seeing other examples on here, I tried to do it myself. I got .05 m/min but the online system I do my homework on, said it was wrong.

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  3. I plugged in your numbers to Damon's solution and got 40 cm/min

    What work do you have to show?

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  4. I tried that but that was wrong too.

    Q= 0.2 m^3/min
    A=surface area= length(width) at 10 cm deep depth is 1/2 the height. Width= 30 + 1/2(70-30)= 50 cm or .5 m

    dh/dt= QA

    A= 5(.5)= 2.5 m^3

    dh/dt= (.2)(2.5)= .05 m/min

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