$3-3$ A horizontal pipe having a surface temperature of $67C$ and diameter of $25cm$ is buried at a depth of $1\mathrm{.}2m$ in the earth at a location where $k=1\mathrm{.}8\frac{W}{m}*C.$ The earth surface temperature is $15C.$ Calculate the heat lost by the pipe per unit length.

in solution, s$=2$piL$/$cosh$-1($D$/$r$),$ but i can not understand why it does, becase D is over than $3$r$,$ i think s$=2$piL$/$ln$($D$/$r$)$ please explain