An inverted right circular cone (pointed end down) has a height of and a top radius of

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

Problem

An inverted right circular cone (pointed end down) has a height of

12\text{ ft}

and a top radius of

5\text{ ft}

. Water flows into the cone at

3\text{ ft}^3\!/\text{min}

while leaking out at

1\text{ ft}^3\!/\text{min}

. At the moment when the water depth is

6\text{ ft}

, what is the rate of change of the water depth? (a)

\dfrac{12}{25\pi}\text{ ft}\!/\text{min}

(b)

\dfrac{8}{25\pi}\text{ ft}\!/\text{min}

(c)

\dfrac{16}{25\pi}\text{ ft}\!/\text{min}

(d)

\dfrac{24}{25\pi}\text{ ft}\!/\text{min}