A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant k is positive). Suppose that r(t) is the radius of the liquid cone at time t. The time after which the cone is empty is

Explanation

To solve the problem of determining the time after which the cone is empty, we will follow these steps:

### Step 1: Set up the relationship between volume and surface area
The volume \( V \) of a right circular cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the liquid cone at time \( t \) and \( h \) is the height of the liquid cone at that time.
...