A double ring test for a given soil and day resulted in an initial infiltration rate of

$3\mathrm{.}0$ in$/$hr$,$ an ultimate infiltration rate of $0\mathrm{.}5$ in$/$hr and a derived decay constant, k $=2\mathrm{.}0$

$(1/$hr$).$ If the inner ring diameter was $12,$ estimate how much water had to be added to

the ring up through the second hour of the test.