SOLUTION: Water is pouring into an inverted cone at the rate of 3.14 cubic meters per minute. The height of the cone is 10 meters, and the radius of its base is 5 meters. How fast is the wat

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Water is pouring into an inverted cone at the rate of 3.14 cubic meters per minute. The height of the cone is 10 meters, and the radius of its base is 5 meters. How fast is the wat      Log On


   

Question 650797: Water is pouring into an inverted cone at the rate of 3.14 cubic meters per minute. The height of the cone is 10 meters, and the radius of its base is 5 meters. How fast is the water level rising when the water stands 7.5 meters above the base?
Answer by Alan3354(69443) About Me  (Show Source):
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Water is pouring into an inverted cone at the rate of 3.14 cubic meters per minute. The height of the cone is 10 meters, and the radius of its base is 5 meters. How fast is the water level rising when the water stands 7.5 meters above the base?
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"when the water stands 7.5 meters above the base" implies the point is at the top, not inverted. r = h/2 if h is measured from the point of the cone.
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V+=+pi%2Ar%5E2h%2F3
r = h/2
V+=+pi%2Ah%5E3%2F12
dV%2Fdt+=+3pih%5E2%2F4%2A%28dh%2Fdt%29 = 3.14 m^3/min
Using the 3.14 for pi
dh/dt = 4/(3h^2) m/min
dh/dt = 4/(3*56.25) = 0.0237 meter/minute