Water is being poured into an inverted right circular conical tank at a constant rate of

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

10\pi\,\text{m}^3/\text{min}

. The tank is 12 m deep and 4 m wide at the top. Water leaks out through a hole in the bottom at a rate of

3h^{2}\,\text{m}^3/\text{min}

, where

h

is the depth (in meters) of the water at that instant. Determine the depth

h

at which the amount of water in the tank is neither increasing nor decreasing.