SOLUTION: A closed box with a square base of side x inches is to hold 125 cubic inches. Write the surface area S of the box as a function of x.

Algebra ->  Equations -> SOLUTION: A closed box with a square base of side x inches is to hold 125 cubic inches. Write the surface area S of the box as a function of x.      Log On


   

Question 1196522: A closed box with a square base of side x inches is to hold 125 cubic inches. Write the surface area S of the box as a function of x.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

Surface area is the lateral area  PLUS doubled base area  2x^2.


Lateral area is the perimeter of the base 4x multiplied by the height 125%2Fx%5E2,  
i.e.  %284x%29%2A%28125%2Fx%5E2%29 = 500%2Fx square inches.


Therefore, the total surface area of the closed box is  500%2Fx + 2x%5E2  square inches.    ANSWER

Solved.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
dimensions x by x by y;
volume, x%5E2y=125
y=125%2Fx%5E2



Surface Area
4xy%2B2x%5E2
4x%28125%2Fx%5E2%29%2B2x%5E2
%284%2A125%29%2Fx%2B2x%5E2
highlight%28500%2Fx%2B2x%5E2%29