A spherical snowball melts so that its surface area is decreasing at when its radius is

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

Problem

A spherical snowball melts so that its surface area is decreasing at

20\text{ cm}^2\!/\text{min}

when its radius is

8\text{ cm}

. What is the corresponding rate of change of the volume at that instant? (a)

-160\text{ cm}^3/\text{min}

(b)

80\text{ cm}^3/\text{min}

(c)

-80\text{ cm}^3/\text{min}

(d)

-20\text{ cm}^3/\text{min}