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.
Answer: Let the length, width, and height of the rectangular box be l, w, and h respectively. Since the bottom is square, we have l = w = x. The surface area of the box is given by:
SA = 2lw + 2lh + 2wh
Substituting l = w = x, we get:
SA = 2x^2 + 2xh + 2xh
SA = 2x^2 + 4xh
Solving for h, we get:
h = (a - 2x^2)/(4x)
The volume of the box is given by:
V = lwh = x^2 * h
V = x^2 * (a - 2x^2)/(4x)
V = (1/4)x(a - 2x^2)
Therefore, the formula for the volume of the box as a function of x with constant a is:
V(x) = (1/4)x(a - 2x^2)