Question

An open rectangular box with a square bottom must have a surface area of A square inches. Write a formula for the volume of the box as a function of x. Your answer will also include the constant, A.

Image of problem is attached.

Answer 1

A= X x X
Volume= A x H

Answer 2

The surface area of the box is being referred to as A
The surface area will be the sum of the four rectangular sides' areas and the base area.
Base area = x²
Rectangular side area = xh
A = x² + 4xh
Volume is, as you said,
V = x²h
Lets substitute h from the formula of A to obtain A in our final answer. Substituting x is possible, but more difficult
(A - x²)/4x = h
V = (x²) * (A - x²)/4x
V = (Ax - x³)/4