Everything about a circle follows from its radius and the constant π, which is the ratio of any circle’s circumference to its diameter. That ratio is the same for every circle, which is the whole reason π is interesting.
The arc and sector formulas require θ in radians, not degrees. One radian is the angle that cuts an arc equal in length to the radius, so a full turn is 2π radians. Converting is a matter of multiplying degrees by π/180.
Area scales with the square
Double the radius and the circumference doubles, but the area quadruples. A 16-inch pizza has 78% more food than a 12-inch one, not 33% more, which makes the larger size almost always better value.
Why radians exist at all
Degrees are arbitrary — 360 is a historical choice with no mathematical basis. Radians make the formulas clean and, more importantly, make calculus work: the derivative of sin x is cos x only when x is measured in radians. In any degrees-based version an awkward factor of π/180 appears everywhere.