The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius.
Exploration was very important for many reasons. Some of those reasons would include finding good and new land for plantations and colonies, making maps, picking what is needed and what is not for expansion. It was all unknown land so they needed as much information possible in order to make better use of their resources.
