A vertical cylindrical tank with radius 2 m is being filled with water at 120 L/min

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

Problem

A vertical cylindrical tank with radius 2 m is being filled with water at 120 L/min, but a leak allows water to escape at a rate of

2h

L/min, where

h

is the water height in meters. When

h = 3\text{ m}

, what is

\dfrac{dh}{dt}

? (Use

1\text{ m}^3 = 1000\text{ L}

.) (a)

-\dfrac{0.114}{4\pi}\text{ m/min}

(b)

\dfrac{0.126}{4\pi}\text{ m/min}

(c)

\dfrac{0.114}{\pi}\text{ m/min}

(d)

\dfrac{0.114}{4\pi}\text{ m/min}