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What is the formula that relates circumference and radius?

A. [tex]C = 2 \pi r[/tex]
B. [tex]C + 2 = 2 \pi r[/tex]
C. [tex]C = 2 \pi D r[/tex]
D. [tex]C = 2 \pi / r[/tex]


Sagot :

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]