Question

A water trough is 10 m long and a cross-section has the shape of an isosceles triangle that is 1 m across at the top and is 50 cm high. The trough is being filled with water at a rate of 0.4 m3/min. How fast will the water level rise when the water is 40 cm deep?

Answer 1

Water level is rising at rate of 0.0143 m/min or 1.43 cm/min

Answer 2

@MTALHAHASSAN2 I would have solved like this,

Given:
dv/dt = 0.4 m^3/min
h=0.4

Goal: find dh/dt

V=.5(lwh)

= .5(10)(2h)h

So V=10h^2

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V=.5(lwh)

dV/dt = 2(10)(h)(dh/dt)

.4 =2(10)(0.4)(dh/dt)

dh/dt =0.05 or 1/20 m/min