Conical Tank Related Rates

Question

A conical tank has height 3 m and radius 2 m at the top. Water level is rising at a rate of 1.7 m/min when it is 2.2 m from the bottom of the tank. At what rate is water flowing in? (Round your answer to three decimal places.)

Answer 1

Let y be height from the bottom and r the radius

The cone has the constraint the at all times (2/3)y = r because the height to radius ratio is 3:2 for all heights.

The Volume relationship with r and h is V(r,y) = (1/3)πr²(y)

Sub in for r: V = (1/3)π(y²4/9)y (4π/27)y³

Take the derivative with time: dV/dt = (4π/9)y²(dy/dt)

You can plug into the equation to solve for dV/dt in m³/min

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