Hello, orochimaru700!

1) Find the waste in making the largest possible cylindrical rod

from a bar of iron 3ft long which has a cross section whose diagonal is 6 inches. I will assume that the bar has a *square* cross-section. Code:

*-----------*
| * |
| 6 * |
| * | x
| * |
| * |
*-----------*
x

The diagonal is 6 inches.

We have: .

The side of the square is: . inches.

The volume of the bar is: .

Code:

_
: - - - 3√2 - - - :
*-------*-*-*-------*
| * * |
| * * |
|* *|
| |
* *
* * - - - - *
* r *
| |
|* *|
| * * |
| * * |
*-------*-*-*-------*
: - r - :

We see that the radius of the cylinder is *half* the side of the square:

. .

The volume of the cylinder is: .

The waste is: .