If 30,000 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. g

The largest possible volume of the box is 500,000 cm³    

Step-by-step explanation:

Let the a side of the square base = x

let the height of the box, = h

volume of the box, v = hx²

Surface area of the box, A = 4hx + x²

                                         30000 = 4hx + x²

make h the subject of the formula;

Volume of the box, V = hx²

At maximum value of V, dv/dx = 0

Substitute in the value of x to determine the maximum volume, V;

Therefore, the largest possible volume of the box is 500,000 cm³