Question

A conical tank has height 3 m and radius 2 m at the top. Water level is rising at a rate of 1.8 m/min when it is 1.5 m from the bottom of the tank. At what rate is water flowing in? (Round your answer to three decimal places.)

Answer 1

5.655 m³/min

Explanation:

Halfway from the bottom of the tank, the radius is half that at the top, so is 1 m. That means the surface area of the water at that point is ...

A = πr² = π(1 m)² = π m²

The rate of flow of water into the tank is the product of this area and the rate of change of depth:

flow rate = area × (depth rate of change)

= (π m²) × (1.8 m/min) = 1.8π m³/min

flow rate ≈ 5.655 m³/min