To answer the question "What is the formula that relates circumference and radius?", let's first recall the standard relationships between different parts of a circle.
The circumference [tex]\( C \)[/tex] of a circle is the distance around the circle's edge. The radius [tex]\( r \)[/tex] of a circle is the distance from the center of the circle to any point on its circumference.
The correct formula that relates the circumference ([tex]\( C \)[/tex]) to the radius ([tex]\( r \)[/tex]) of a circle is:
[tex]\[ C = 2 \pi r \][/tex]
Where:
- [tex]\( C \)[/tex] is the circumference
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159
- [tex]\( r \)[/tex] is the radius
Given this, let's evaluate the options one by one:
A. [tex]\( C = 2 \pi r \)[/tex]
This is the correct formula, as explained above.
B. [tex]\( C + 2 = 2 \pi r \)[/tex]
This formula incorrectly suggests adding 2 to the circumference, which is not part of the established relationship.
C. [tex]\( C = 2 \pi D r \)[/tex]
This formula introduces an extraneous [tex]\( D \)[/tex] (perhaps intending diameter), but as written, it complicates and incorrectly represents the relationship.
D. [tex]\( C = 2 \pi / r \)[/tex]
This formula incorrectly suggests dividing [tex]\( 2\pi \)[/tex] by the radius, which is not how the circumference is calculated.
Therefore, the correct option is:
A. [tex]\( C = 2 \pi r \)[/tex]
