SOLUTION: A container is to be designed that is a rectangilar box with an open top that will hold 108 cubic inches. If x= the length of the side of the base, then express the surface area o
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Question 147149: A container is to be designed that is a rectangilar box with an open top that will hold 108 cubic inches. If x= the length of the side of the base, then express the surface area of the box as a function of X. What is domain of this function and determine the dimensions of the box that minimizes the surface area of the box
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A container is to be designed that is a rectangular box with an open top that will hold 108 cubic inches. If x = the length of the side of the base, then express the surface area of the box as a function of X. What is domain of this function and determine the dimensions of the box that minimizes the surface area of the box
:
Assume the base is square with an area = x^2.
:
Let h = height of the box
:
The volume equation
x^2 * h = 108
h =
:
Surface area:
Bottom = x^2
4 sides = 4(x) = ; area of the 4 sides
:
S.A. = x^2 +
:
Graph: y = x^2 +
:
Min surface area: x = 6
Find h = = 3 inches
:
min surface area of the box: 6^2 + 4(6*3) = 108 sq inches
:
Interesting that the vol and surface area are equal.
:
Domain of the equation: x > 0
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