SOLUTION: A closed box with a square base is required to have a volume of 10 feet. 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

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Question 312536: A closed box with a square base is required to have a volume of 10 feet.
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 A = A(x). For what value x is A smallest?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A closed box with a square base is required to have a volume of 10 feet.
:
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.
Vol: x^2*h = 10
h = 10%2Fx%5E2
;
Amt of material is the surface area
S.A. = 2x^2 + 4(x*h)
Replace h with 10%2Fx%5E2
S.A. = 2x^2 + 4(x*10%2Fx%5E2)
S.A. = 2x^2 + 4(10%2Fx)
f(x) = 2x^2 + (40%2Fx); amt of material as a function of x
:
B) How much material is required for a base 1 foot by 1 foot?
f(1) = 2(1^2) + 40/1
f(1) = 42 sq/ft
:
C)How much material is required for a base 2 feet by 2 feet?
f(2) = 2(2^2) + 40/2
f(2) = 8 + 20
f(2) = 28 sq/ft
:
D Graph A = A(x). For what value x is A smallest?
:
+graph%28+300%2C+200%2C+-4%2C+8%2C+-10%2C+50%2C+2x%5E2%2B%2840%2Fx%29%29+
:
Looks like min surface area is x=2
:
Check our solutions, by finding the vol when x=2
h = 10/2^2
h = 2.5
:
Vol = 2*2*2.5 = 10 cu/ft