A right circular cone has height and radius at its top

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

Problem

A right circular cone has height

12\text{ cm}

and radius

6\text{ cm}

at its top. Water is poured in so that the depth

h

of the water increases at a constant

0.50\text{ cm/s}

. When the water is

4\text{ cm}

deep, what is the rate at which the water’s volume is increasing? (a)

4\pi\text{ cm}^{3}\!/\!\text{s}

(b)

\dfrac{8\pi}{3}\text{ cm}^{3}\!/\!\text{s}

(c)

2\pi\text{ cm}^{3}\!/\!\text{s}

(d)

6\pi\text{ cm}^{3}\!/\!\text{s}