If 19,200 cm of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Step 1 We are given that the box has a square base and an open top. Let b represent the length of the box's base and let h represent the height of the box, each measured in cm. Let V represent volume of the box, measured in cm. Writing an equation for V in terms of b and h gives us the following. v = 256000 x cm Let S represent the surface area of the box, measured in cm. Writing an equation for S in terms of b and h gives us the following. S= b+4bh cm