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?

Question

carlyleukhardt · Answer

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

koikkara · Answer

@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

--------------
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