Problema Solution
United Parcel Service has contracted you to design a closed box with a
square base that has a volume of 10,000 cubic inches.
Express the surface area S of the box as a function of x.
Answer provided by our tutors
Let
x = the length of the side of the square base
h = the height of the box
V = 10,000 in^3 the volume of the box
S = the surface area of the box
V = x^2*h
x^2*h = 10,000
h = 10,000/x^2
The surface are of the box is (we will assume the box has a cover):
S = 2x^2 + 4*xh
Plug for h = 10,000/x^2
S = 2x^2 + 4x*10,000/x^2
S = 2x^2 + 40,000/x
The surface area S of the box as a function of x is S = 2x^2 + 40,000/x.