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An open box with a square base is to ...

An open box with a square base is to be made out of a given quantity of card board of area `c^2` square units. Show that the maximum volume of the box is `(c^3)/(6sqrt(3))` cubic units.

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To solve the problem of finding the maximum volume of an open box with a square base made from a given area of cardboard \( c^2 \), we can follow these steps: ### Step 1: Define the Variables Let the side length of the square base be \( x \) and the height of the box be \( y \). ### Step 2: Write the Volume Formula The volume \( V \) of the box can be expressed as: \[ ...
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