why does the filter paper must have a smaller radius than the funnel?

Answer 1

In any gravimetric analysis, you must watch out for material losses. This has a drastic effect on your calculations and accuracy.

Note that paper has an interesting characteristic of WICKING effect. And so is the glass. Remember the meniscus line in burettes or cylinders? Any material at the edge and the funnel being wet at the rim, will most likely travel outside of the paper and may slip out of the funnel by simple gravity. By making the paper smaller, then during washing of the precipitates, there is LESS likely chance for material losses.

Unless, you're really sloppy.

Answer 2

or else it will stick out the top and be easy to tear.