Answer:
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