An open box, with a square base, is to be made out of a given quantity of metal sheet of area `C^2.` Show that the maximum volume of the box is `C^3/(6sqrt3)`

Explanation

To solve the problem of finding the maximum volume of an open box with a square base made from a given area of metal sheet \( C^2 \), we will follow these steps:

### Step 1: Define Variables
Let the side length of the square base be \( x \) and the height of the box be \( h \).

### Step 2: Write the Volume Formula
The volume \( V \) of the box can be expressed as:
\[
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