To determine which formula should be used to find the circumference of a circle, let's carefully analyze the options provided. The standard formula for the circumference [tex]\( C \)[/tex] of a circle involves a relationship with its radius [tex]\( r \)[/tex] or its diameter [tex]\( d \)[/tex].
1. Relationship with the Radius:
The circumference of a circle can be defined as:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Relationship with the Diameter:
The diameter [tex]\( d \)[/tex] of a circle is twice the radius:
[tex]\[
d = 2r
\][/tex]
Substituting [tex]\( d \)[/tex] in the circumference formula above, we get:
[tex]\[
C = 2 \pi r = \pi d
\][/tex]
This shows that the circumference can also be expressed in terms of the diameter [tex]\( d \)[/tex].
Now, evaluating each given formula:
- [tex]\( C = \pi d \)[/tex]: This formula is correct as it directly relates the circumference to the diameter [tex]\( d \)[/tex].
- [tex]\( C = 2 \pi d \)[/tex]: This formula is incorrect because it incorrectly doubles the factor [tex]\( \pi d \)[/tex].
- [tex]\( C = \pi r \)[/tex]: This formula is incorrect because it omits the necessary factor of 2 that accompanies [tex]\( \pi r \)[/tex].
- [tex]\( C = \frac{\pi}{d} \)[/tex]: This formula is incorrect because it inaccurately associates circumference inversely with the diameter.
Given these explanations, the correct formula from the options provided is:
[tex]\[
C = \pi d
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C = \pi d} \][/tex]
In the list provided, this corresponds to answer:
[tex]\[ \boxed{1} \][/tex]
