SOLUTION: Hi, I am working on this problem, am stuck and would appreciate help! Constructing an open box An open box with a square base is required to have volume of 10 cubic ft. a) Ex

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Question 72562This question is from textbook College Algebra Essentials
: Hi, I am working on this problem, am stuck and would appreciate help!
Constructing an open box
An open box with a square base is required to have volume of 10 cubic ft.
a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.
b) How much material is required for a base 1 foot by 1 foot?
c) How much material is required for a base 2 feet by 2 feet?
d) Graph . For what value of x is A smallest?
Thanks for your help!
Jodi This question is from textbook College Algebra Essentials

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
An open box with a square base is required to have volume of 10 cubic ft.
:
a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.
:
Base area * height = 10 cu ft
x^2 * h = 10
h = 10/x^2 is the height
:
Area of the 4 sides:
4(x*h)
Replace h with (10/x^2)
4(x*10/x^2)
Simplify:
4(10/x)
Area of the 4 sides = 40/x
:
Total area:
A = x^2 + 40/x
:
:
b) How much material is required for a base 1 foot by 1 foot?
A = 1^2 + (40/1)
A = 41 sq ft
:
c) How much material is required for a base 2 feet by 2 feet?
A = 2^2 + (40/2)
A = 24 sq ft
:
d) Graph A=A(x). For what value of x is A smallest?
A = x^2 + (4/x)

:
Looks like the min area is x ~ 2.7 ft for an area of about 22 sq ft