a conical tank opened at the top is 4m high and a top radius of 1m. its is filled with water and after 2 hours, the depth of the water dropped to 1m due to evaporation. set up a differential equation for the depth of water as a function of time and solve for its expression of depth of h
using similar triangles, we see that r = h/4
The rate of evaporation is proportional to the surface area of the water, so
so, what is dA/dt?
A = πr^2 = π/16 h^2
dA/dt = π/8 h dh/dt
see what you can do with that.
(t)
Differential equation:
dh/dt = -k
where k is the rate of evaporation.
Solution:
h(t) = 4 - kt