A trough is 14 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1
ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 4 inches deep?
1 answer:
Step-by-step explanation:
Using similar triangles, the height and width of the water is proportional to the height and width of the trough.
w / h = 5 / 1
w = 5h
The volume of the water is:
V = AL
V = (½ wh) (14)
V = 7wh
Substituting:
V = 7(5h)h
V = 35h²
Take derivative with respect to time:
dV/dt = 70h dh/dt
Given that dV/dt = 15 and h = ⅓:
15 = 70 (⅓) dh/dt
dh/dt = 9/14
dh/dt ≈ 0.643 ft/min
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