SOLUTION: You are given one scrapbook page (12 inches by 12 inches). With only this for your material, you must create a container that will maximize volume while minimizing the total area.

Algebra ->  Surface-area -> SOLUTION: You are given one scrapbook page (12 inches by 12 inches). With only this for your material, you must create a container that will maximize volume while minimizing the total area.      Log On


   

Question 449938: You are given one scrapbook page (12 inches by 12 inches). With only this for your material, you must create a container
that will maximize volume while minimizing the total area.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think the answer might be to cut 4 x 4 inch squares out of each corner.
If you then fold the sides up, you have a 4 x 4 x 4 box open on top.
the volume is +4%2A4%2A4+=+64+ in3
The area is +5%2A4%2A4+=+80+ in2
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Call the squares cut out of the corners +x%5E2+
The surface area is then +A+=+144+-+4x%5E2+ in2
The volume is then x%2A+%2812+-+2x%29%5E2+
-----------------------------------
Suppose I removed 3.99 x 3.99 in2 from each corner
V+=+3.99%2A+%2812+-+2%2A3.99%29%5E2+
V+=+3.99%2A+%2812+-+7.98%29%5E2+
V+=+3.99%2A+4.02%5E2+
+V+=+64.48+
and
+A+=+144+-+4%2A15.92+
+A+=+144+-+63.68+
+A+=+80.32+
Both volume and area went up.
Now try +x+=+4.01+
If either volume goes down or area goes up,
my guess is right