A common 6-in.-radius soccer ball contains 12 pentagons arranged so that every pentagon is separated from the next by the same arc length as one of the spherical (great circle segment) sides of the regular hexagons. As the hexagons are regular, this is the same arc length as one of the sides of the pentagons, as the pentagons also border the hexagons.
Calculate the arc length of a pentagon's side of a new soccer ball using the same radius and instead of one line of separation between pentagons, use two lines of separation between pentagons and consider every new line with a distance equal to a side of a pentagon.
(See picture)
Note: The endpoints of the mentioned lines intersect with the surface of the soccer ball or sphere.
(In reply to
re: solution by SilverKnight)
Ahhhh.... I did misunderstand what you wrote.
You are analyzing the arc length of the side of "one spherical triangular face"--not, as I suggested, one of 5 equilateral triangles.
Your calculation looks correct to me.
- SK
re(2): solution
