Water is leaking out of an inverted conical tank at a rate of13400cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height8meters and the diameter at the top is6meters. If the water level is rising at a rate of24centimeters per minute when the height of the water is5meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

9514 1404 393

  2,664,118.8 cm³/min

Step-by-step explanation:

The diameter at the water level of 5 m is (5/8)(6 m) = 3.75 m, so the area of the water surface is ...

  A = (π/4)d² = (π/4)(3.75 m)² ≈ 11.044662 m²

When rising at the rate of 24 cm/min, the volume is increasing at the rate ...

  (110,446.62 cm²)(24 cm/min = 2,650718.8 cm³/min

The input volume must be sufficient to accommodate this increase as well as the leakage. Then the input volume is ...

  2,650718.8 cm³/min + 13,400 cm³/min = 2,664,118.8 cm³/min

there are infinitely many solutions.