SOLUTION: An open rectangular box with volume 7 m3 has a square base. (a) Express the surface area of the box as a function of the length (x) of a side of the base.

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Question 342278: An open rectangular box with volume 7 m3 has a square base.
(a) Express the surface area of the box as a function of the length (x) of a side of the base.
Found 2 solutions by ankor@dixie-net.com, nyc_function:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
An open rectangular box with volume 7 m3 has a square base.
:
(a) Express the surface area of the box as a function of the length (x) of a side of the base.
:
Find the height using the given volume:
x^2 * h = 7
h =
:
Surface area of an open box
S.A. = x^2 + 4(x*h)
;
Replace h with
S.A. = x^2 + 4(x*)
;
Cancel x:
S.A. = x^2 + 4()
:
f(x) = x^2 + ; is the surface area in terms of x

Answer by nyc_function(2741) (Show Source):
You can put this solution on YOUR website!
volume = length * width * height
square base ... let length and width = x
x^2 * height = 7
height = 7 / x^2
Surface area (with open top) = bottom + 4 sides
Surface area = x^2 + 4 * x * height
. . . we already know height = 7 / x^2, so substute
Surface area = x^2 + 4x * 7 / x^2
Surface area = x^2 + 28 / x <=======