The task involves identifying a design that will not work as a stencil for spray painting the word 'pedagogy'. When designing stencils, areas within enclosed shapes like 'p', 'a', 'o', 'g', and 'd' must remain attached to the rest of the stencil, otherwise, these central parts (called 'counters') would fall out. Therefore, a stencil is successful if it includes bridges or connectors to retain these counters.
When evaluating the given designs:
- Fig 1: Includes bridges, preserving counters adequately.
- Fig 2: Also includes necessary bridges.
- Fig 3: Lacks bridges, making counters fall out, thus not preserving inner shapes.
- Fig 4: Uses bridges effectively to keep parts in place.
Therefore, the design in Fig 3 will NOT function as a stencil for spray painting the word 'pedagogy' since it does not adequately use bridges to retain the counters of the letters correctly, resulting in missing inner parts when painted.