A water trough is 10m long and a cross-section has...

A water trough is 10m long and a cross-section has the shape of anisosceles trapazoid that is 40cm wide at the bottom, 75cm wide atthe top, and has a height of 55cm. If the trough is being filledwith water at the rate of 0.7m^3 /min, how fast is the water levelrising when the water is 45cm deep? (Round the result to thenearest hundreth)

I get the answer of 8.2cm/min when I work this out, its supposed tobe over 10 cm/min though. If someone could work this out please I'dappreciate it.

dv/dt = .7 m^3/min
h= .45
Height = .4 + h
total area of filled .5(.8 + h)h => (h^2 +.8h)/2

volume = 5(h^2 + .8h)

dv/dt = 5(2h + .8) dh/dt

.7 = 5(2 * .45 + .8) dh/dt

dh/dt = .7 / 8.5
dh/dt= .8235m^3/min
dh/dt= 8.24cm^3/min
Have no idea where I went wrong. Thank you for the help.

Answers ( 1 )

  1. jonatã alves
    jonatã alves
    V = (b1+b2)h / 2
    b1 = .4
    b2 = .4 +2(.175/.55)h      (bysimilar triangles)
    V = 5(.4 + 2(.35/.55)h)h
        = 2h + 1.75h^2 / .55
    dV/dt = 2dh/dt +3.5h/.55 dh/dt
    dh/dt = .7 /(2 + (3.5/.55)(.45)) = .1439m/min
                                                    =14.39cm/min

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