SOLUTION: Please help me solve this problem: A closed box is to be constructed with square ends. The surface area of the box is 1000 square inches. Express its volume as a function of the le

Algebra ->  Surface-area -> SOLUTION: Please help me solve this problem: A closed box is to be constructed with square ends. The surface area of the box is 1000 square inches. Express its volume as a function of the le      Log On


   

Question 896548: Please help me solve this problem: A closed box is to be constructed with square ends. The surface area of the box is 1000 square inches. Express its volume as a function of the length of its end.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
h for how tall the box.
x for each side of the top or bottom for the square part.

A for total surface area; A=1000.

A=x%5E2%2Bx%5E2%2B4hx, both x and h are unknown.

V=h%2Ax%5E2, V is unknown.


4hx=A-x%5E2-x%5E2
h=%28A-2x%5E2%29%2F4x
-
V=%28%28A-2x%5E2%29%2F4x%29x%5E2
highlight%28V=%28A-2x%5E2%29x%2F4%29
You could then substitute for given A and further simplify.