Water is pumped into a vertical cylindrical tank at a rate of

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

Problem

5\text{ m}^3\!/\text{min}

. The tank has an interior radius of

2\text{ m}

. At the instant when the depth of the water is

3\text{ m}

, what is the rate at which the water level is rising? (a)

\dfrac{5}{4}\text{ m}\!/\text{min}

(b)

\dfrac{5}{4\pi}\text{ m}\!/\text{min}

(c)

\dfrac{5}{2\pi}\text{ m}\!/\text{min}

(d)

\dfrac{5}{8\pi}\text{ m}\!/\text{min}