Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is `K >0` is

Options

A. `(dr)/(dt)+ K=0`
B. `(dr)/(dt) -K =0`
C. `(dr)/(dt) = Kr`
D. None of these

Explanation

To derive the differential equation corresponding to the rate of change of the radius of a spherical raindrop that evaporates at a rate proportional to its surface area, we can follow these steps:

### Step 1: Understand the volume and surface area of a sphere
The volume \( V \) of a spherical raindrop with radius \( r \) is given by:
\[ V = \frac{4}{3} \pi r^3 \]
The surface area \( S \) of the spherical raindrop is given by:
...