# Thread: help please i am doing a pre uni course and am stuck on this

1. ## help please i am doing a pre uni course and am stuck on this

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

2. Originally Posted by alpharebel10
A rectangular block of metal with a square cross section has a total surface area of 240cm. find the total volume of the box.
The volume V of a rectangular prism with length L, height h, and width w is given by V = Lhw.

In this particular case, L = w, so V = hw^2.

The total surface area SA is the sum of the areas of all six faces, or SA = 2Lw + 2Lh + 2hw. Since L = w, then:

SA = 2w^2 + 4wh = 240

Solve the above for h in terms of w.

Plug the result into the "volume" formula. This will allow you to find an expression for the volume in terms only of w.

(Since you haven't been given enough information, there is no way to find the numerical value of the volume.)