A rectangular block of metal with a square cross section has a total surface area of 240cm. find the total volume of the box .

using

vol= ab squr

Area= 4ab+ bsqur

i can find the max volume wil be 357.75 when a=4/5/12 and b=9

but i did a question this way on another test and got no points as i have to use differentation

i can do it if im given the volume and have to find the area by

-4v+ b squr = 0

bsqur

but dont know how to change it round to find vol when given area

any help would be greatfull ty