How fast is the water level rising when the water is 2m deep?

Question

a horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a lower base of 4m, and an upper base of 6m. water is being poured into the trough at the rate of 10m3/min. how fast is the water level rising when the water is 2m deep?

(this is about calculus)

(topic about: Related Rates)

(pls. help me to answer this question)

(pls. show your solution)

(thanks)

Answer 1

I'm not going to solve it for you, but your first step would be to find the area of the trough.  

Answer 2

Let:

w = width of the water surface at any given depth of the contained water

h = the depth of the contained water

dh/dt = rate of change in depth of water

dV/dt = rate of change in volume of contained water

dV = change in volume

w = 4 + h/2

dV = 16wdh

16wdh/dt = 10

dh/dt = 10/(16w) = 5/(8(4 + h/2))

If h = 2

dh/dt = 5/(8(4 + 2/2) = 1/8 m/min