# 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.

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.

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

Let’s 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