A spherical raindrop evaporates at a rate proportional to its surface area.If V = volume of the raindrop and S = surface area, which of the following is a differential equation for $\frac{d V}{d t}$ ?
A) $\frac{d V}{d t}=k S$ with k a negative constant
B) $\frac{d V}{d t}=\frac{k}{S}$ with k a negative constant
C) $\frac{d V}{d t}=k S$ with k a positive constant
D) $\frac{d V}{d t}=\frac{k}{S}$ with k a positive constant

Question

Quizplus · Accepted Answer

The rate of evaporation is directly proportional to the surface area, so $\frac{d V}{d t}=k S$ is correct. Since the raindrop is evaporating, the constant $k$ must be negative, indicating a decrease in volume over time.

A Spherical Raindrop Evaporates at a Rate Proportional to Its dVdt\frac{d V}{d t}dtdV​

A Spherical Raindrop Evaporates at a Rate Proportional to Its $\frac{d V}{d t}$