Question

United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches.
A.) Express the surface area S of the box as a function of x?

Answer 1

let the length of 1 side of the base be x height = h

then the volume V = x^2h

using the given information then

5000 = x^2h

let h = 5000/x^2


Surface area... not top



the box has dimensions x, x, h

base = x^2 4 sides all have same area xh

so surface area s = x^2 + 4xh

use the substitution h = 5000/x^2

then s = x^2 + 4x(5000/x^2)

or s = x^2 + 20000/x