A cylindrical tank with a fixed radius of 3 m is partially filled with water

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A cylindrical tank with a fixed radius of 3 m is partially filled with water. Water flows into the tank at 6 m

^{3}

/min while simultaneously leaking out at 2 m

^{3}

/min. When the water depth is 1.5 m, what is the instantaneous rate of change of the depth? (a)

\dfrac{6}{9\pi}\text{ m/min}

(b)

\dfrac{4}{3\pi}\text{ m/min}

(c)

\dfrac{4}{9\pi}\text{ m/min}

(d)

\dfrac{2}{9\pi}\text{ m/min}