A three$-$point bending test was performed on an aluminum oxide specimen having a circular cross section of radius $4\mathrm{.}6$ mm ; the specimen fractured at a load of $4460$ N when the distance between support points was $47$ mm $.$ Another test is to be performed on a specimen of this same material, but one that has a square cross section of $15$ mm in length on each edge. At what load would you expect this specimen to fracture if the support point separation is maintained at $47$ mm $?$

$F_f=$ N