Water is being pumped into a cylindrical tank of radius 2 m at a rate of 6 m /min

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

Problem

Water is being pumped into a cylindrical tank of radius 2 m at a rate of 6 m

^3

/min. At the same time, water leaks from a hole in the bottom at a rate of

4\sqrt{h}

^3

/min, where

h

is the water depth (in meters). For what water depth will the height of the water in the tank stop rising? (a)

1.50\text{ m}

(b)

2.56\text{ m}

(c)

2.25\text{ m}

(d)

3.0\text{ m}