Water drains from the bottom of an inverted right circular cone at a constant rate of

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

Problem

12\pi\,\text{cm}^3\,\text{s}^{-1}

. The cone itself has fixed height

30\,\text{cm}

and base radius

15\,\text{cm}

. At the instant when the water depth is

9\,\text{cm}

, find the rate, in cm s⁻¹, at which the depth of the water is decreasing.