To determine the formula that correctly relates the circumference ([tex]\(C\)[/tex]) and the radius ([tex]\(r\)[/tex]) of a circle, we need to consider the definitions and standard formulae within geometry.
The circumference of a circle is the distance around the circle's edge. One of the fundamental relationships in circle geometry is that the circumference is directly proportional to both the radius and the constant [tex]\(\pi\)[/tex] (pi).
Let's examine each option:
A. [tex]\( C = 2 \pi r \)[/tex]
- This formula states that the circumference [tex]\(C\)[/tex] is equal to two times [tex]\(\pi\)[/tex] times the radius [tex]\(r\)[/tex]. This is the standard and well-known formula for the circumference of a circle.
B. [tex]\( C = 2 \pi / r \)[/tex]
- This formula implies that the circumference is inversely proportional to the radius, which contradicts the geometric properties of a circle.
C. [tex]\(C + 2 = 2 \pi r \)[/tex]
- This formula includes an additional term [tex]\(+2\)[/tex] on the left side, which is not part of the standard relationship between circumference and radius.
D. [tex]\( C = 2 \pi D r \)[/tex]
- This formula incorrectly introduces an extra variable [tex]\(D\)[/tex], and having [tex]\(D\)[/tex] times [tex]\(r\)[/tex] is incorrect since the circumference should only include a single radius term, not a product of multiple dimensional terms.
The correct formula that accurately represents the relationship between the circumference and radius of a circle is:
[tex]\( \boxed{A. \, C = 2 \pi r} \)[/tex]
Thus, the correct formula relating circumference and radius is [tex]\(C = 2 \pi r\)[/tex].
