▁geometry , ▁the ▁paper ▁bag ▁problem ▁or ▁te ab ag ▁problem ▁is ▁to ▁calculate ▁the ▁maximum ▁possible ▁infl ated ▁volume ▁of ▁an ▁initially ▁flat ▁se aled ▁rect angular ▁bag ▁which ▁has ▁the ▁same ▁shape ▁as ▁a ▁c ush ion ▁or ▁pill ow , ▁made ▁out ▁of ▁two ▁pieces ▁of ▁material ▁which ▁can ▁b end ▁but ▁not ▁stretch . ▁ ▁According ▁to ▁Anthony ▁C . ▁Robin , ▁an ▁approximate ▁formula ▁for ▁the ▁capacity ▁of ▁a ▁se aled ▁expanded ▁bag ▁is : ▁ ▁where ▁w ▁is ▁the ▁width ▁of ▁the ▁bag ▁( the ▁shorter ▁dimension ), ▁h ▁is ▁the ▁height ▁( the ▁longer ▁dimension ), ▁and ▁V ▁is ▁the ▁maximum ▁volume . ▁The ▁approximation ▁ign ores ▁the ▁cr imp ing ▁round ▁the ▁equ ator ▁of ▁the ▁bag . ▁ ▁A ▁very ▁rough ▁approximation ▁to ▁the ▁capacity ▁of ▁a ▁bag ▁that ▁is ▁open ▁at ▁one ▁edge ▁is : ▁▁▁ ▁( This ▁latter ▁formula ▁assumes ▁that ▁the ▁corners ▁at ▁the ▁bottom ▁of ▁the ▁bag ▁are ▁linked ▁by ▁a ▁single ▁edge , ▁and ▁that ▁the ▁base ▁of ▁the ▁bag ▁is ▁not ▁a ▁more ▁complex ▁shape ▁such ▁as ▁a ▁l ens ). ▁ ▁The ▁square ▁te ab ag ▁ ▁In ▁the ▁special ▁case ▁where ▁the ▁bag ▁is ▁se aled ▁on ▁all ▁edges ▁and ▁is ▁square ▁with ▁unit ▁sides , ▁h ▁= ▁w ▁= ▁ 1 , ▁and ▁so ▁the ▁first ▁formula ▁estimates ▁a ▁volume ▁for ▁this ▁of ▁roughly : ▁ ▁or ▁roughly ▁ 0 . 1 9 . ▁According ▁to ▁Andrew ▁Ke pert ▁at ▁the ▁University ▁of ▁New castle