$1-$ A cylindrical cup such as given in question $4$ is produced via slip casting method: the water is absorbed by pastry by time and the decrease rate of the height of slip $d\frac{h}{d}t$ is proportional to the surface area $A.$ a$)$ Write the differential equation and solve $($Find the height change $h$ by time without considering the base $(5$P$)$ b$)$ Repeat the same problem including the basement effect $(10$P$)$

c$)\frac{1}{3}$ of the total volume is emptied in $30$min, how much time is required for $\frac{2}{3}$ of the total volume be emptied $(5$ P$)$

$R=2cm,H=10cm$

d$)$ What will be the wall thickness of the cup after $\frac{1}{3}$ of the volume is emptied? $(5$ P$)$

e$)$ If the wall accumulation rate is inversely proportional to the square root of time, and considering the rate constant is half as in a$,$ find out the wall thickness after $30$min. and compare with $d(5P)($First set the eqn. and solve$)$