Originally Posted by

**lawochekel** A conical tank of height 3m is full of water and the radius of surface is 1m. After 8 hrs the depth of water is 1.5m. If we assume that the water

evaporate at a rate proportional to the surface area expose to the air, obtain a mathematical model for predicting the volume of water in the tank

at any time t.

trying to solve this model since two days, and this is what i have been able to come up with.

factors/variables/parameters

1 radius of conical tank (r)

2 height (h)

3 cross-sectional area $\displaystyle \pi r \sqrt{r^2 + h^2} $

4 volume in t time V(t)

5 rate of evaporation $\displaystyle \frac{1}{2} mv^2 = mgh , v = \sqrt{2gh} $

then i came up with this model formulation

$\displaystyle V(t) = \pi r \sqrt{r^2 + h^2} - \sqrt{2gh} t $ , v in volume, t in hrs