SOLUTION: Seven pencils are held together in a hexagonal shape by an elastic band. If the pencils are of diameter 7 mm, what is the length of the band in this position?

The red arc at the bottom is subtended by a central angle of 60o,
which is π/3 radians. Each circle's diameter is 7 mm, so each circle's 
radius is 7/2 mm. So its length is 



So the length of each round part of the elastic band is .

In the rectangle, the upper side has the length of 2 radii, so the
lower side is also 2 radii or 2*7/2 or 7 mm.

So the length of each straight part of the elastic band is 7 mm.

Since the elastic band has 6 round parts and 6 straight parts, the
length of the elastic band is

.  

Answer = 

Edwin