The surface area of a melting spherical ice sculpture is decreasing at a rate of when…

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

Problem

The surface area of a melting spherical ice sculpture is decreasing at a rate of

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

when its radius is

10\text{ cm}

. At that instant, what is the rate of change of the sphere’s volume? (a)

-40\text{ cm}^{3}\!/\!\text{min}

(b)

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

(c)

-200\text{ cm}^{3}\!/\!\text{min}

(d)

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