a horizontal trough is 16 meters long and its ends are isosceles trapezoids with an altitude of 4 meters, an upper base of 6 meters and lower base of 4 meters. water is being poured in the trough at a rate of 10 cubic meters per minute.

Question

a) how fast is the water level rising when the water is 2 meters deep?
b) if the water level is decreasing at a rate of 25 centimeters per minute when the water is 3 meters deep, at what rate is water being drawn from the trough?

Answer 1

When the height of the water is h, the surface of the water is 4 + h/2 wide
That means the cross-section of the water is a trapezoid with area 4(4 + h/2)/2 * h = 8h+h^2
Thus the volume of the water is
v = 16(8h+h^2)
dv/dt = 16(8+2h) dh/dt = 32(h+4) dh/dt
Now plug in your numbers to find dh/dt or dv/dt