The volume of a sphere is decreasing at a constant rate of

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

Problem

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

. At the moment when the radius is

3\text{ cm}

, what is the instantaneous rate of change of the sphere’s surface area

S

? (a)

-\dfrac{50\pi}{3}\text{ cm}^{2}\!/\text{s}

(b)

+\dfrac{100\pi}{3}\text{ cm}^{2}\!/\text{s}

(c)

-\dfrac{100\pi}{3}\text{ cm}^{2}\!/\text{s}

(d)

-50\pi\text{ cm}^{2}\!/\text{s}