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A water pump is filling up a tank in the shape of an inverted cone. The top of the cone has a diameter of 12 meters, and the cone is 8 meters tall. If the water is being pumped into the cone at a rate of 20 m³ per minute, how fast is the water level rising when the water level’s diameter is 6 m?

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sqdancefan

Answer:

  20/(9π) m/min ≈ 0.707 m/min

Step-by-step explanation:

The rate of change of height is the rate of change of volume divided by the surface area. Of course, the surface area is given by πr², where r = d/2 = 3 m.

  dh/dt = (dV/dt)/A = (20 m³/min)/(π(3 m²))

  dh/dt = 20/(9π) m/min ≈ 0.707 m/min

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