Lengthwise cross$-$section of an ice ring is given below. The dome radius is r$=25$ m$,$ and its suspended with the help of steel wireframe. Assume all walls including dome$-$roof and the ice floor are black and isothermal, and also assume the ice ring is large enough to be treated in two$-$dimensional form as illustrated below. The dome $$ and the ice floor $$ are maintained at constant $17$C and $5$C$,$ respectively. Determine $($a$)$ the view factors between $$ and $,$ and $($b$)$ calculate the net radiation heat transfer rate from the dome to the ice$-$floor.