Mathematics

Problem

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

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}

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

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

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