The figure below shows an open box (a box with no top) with a square base.

Question

The box has a volume of 10 cubic feet. Express the surface area, S, of the box as a function of the length of a side of its square base, x.

Answer 1

V= 10 ft^3 = (x^2)h

h= 10/x^2

Surface Area = A = area of the bottom + 4 times area of the sides

A= x^2 + 4xh = x^2 + 4(x)(10/x^2 = x^2 +40/x

Answer 2

Surface area of the box is 4 times the area of the sides plus the area of the square bottom.

S = 4xy+x²

Volume, V = 10 = yx² --> y = 10/x²

S = 40x/x²+x²

S = 40/x + x³