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A trough is 14 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled withwater at a rate of 11 ft3/min, how fast is the water level rising when the water is 5 inches deep?
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Answer #1

V=(1/2)(bhl) (b=4x, h=x, l=13)


V=.5(4x)(x)(13)
V=26x^2

dV/dt=52x dx/dt (where x represents height in feet)

11=52(4/14) dx/dt
11(14)/[4(52)] = dx/dt

dx/dt=0.74 ft/min

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