A tank is shaped like a frustum of a right circular cone

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

Problem

A tank is shaped like a frustum of a right circular cone. The radius of the circular cross-section varies linearly from

3\,\text{m}

at the bottom (

h=0

) to

5\,\text{m}

at the top (

h=8\,\text{m}

). Water flows into the tank at a constant

6\,\text{m}^3/\text{min}

. Compute

\dfrac{dh}{dt}

when the water depth is

6\,\text{m}

, giving an exact value in

\text{m/min}