Question

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.

Answer 1

9514 1404 393

Answer:

2,664,118.8 cm³/min

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