A dish has a shape described by the equation:

h=(x^2+y^2)^3/2

At time = 0 it is filled to a height of 20cm with a fluid that evaporates when exposed to air. The evaporation rate is proportional to the exposed surface area (that is decreasing) at any time t.

if h(t) is the height of the fluid at time t then

dh/dt is proportional to pir(t)^2, r(t) is the radius at time t. After 20 minutes the height of the fluid was 19.7cm.

im trying to make a differential equation that governs the height h(t) during the evaporation.

initially trying to write h as a function of r

maybe

dh = pi*r^{2}(t) dt???