A right circular cone

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

Problem

A right circular cone,

10\text{ m}

tall with a base radius of

4\text{ m}

, is upright with its vertex at the bottom. When the water depth in the cone is

3\text{ m}

, the depth is increasing at

0.15\text{ m}\!/\text{min}

. At that instant, how fast is the area of the water’s surface increasing? (a)

0.072\pi\text{ m}^2\!/\text{min}

(b)

0.36\pi\text{ m}^2\!/\text{min}

(c)

0.144\pi\text{ m}^2\!/\text{min}

(d)

0.288\pi\text{ m}^2\!/\text{min}