To find the equivalent formula for the circumference of a circle [tex]\( C \)[/tex] when expressed in terms of the diameter [tex]\( d \)[/tex], let's start by recalling the basic relationship between the radius [tex]\( r \)[/tex] and the diameter [tex]\( d \)[/tex] of a circle.
Given:
- [tex]\( r \)[/tex] is the radius of the circle.
- [tex]\( d \)[/tex] is the diameter of the circle.
The relationship between the radius and the diameter is:
[tex]\[ d = 2r \][/tex]
Now, we know the formula for the circumference [tex]\( C \)[/tex] of a circle in terms of its radius is:
[tex]\[ C = 2\pi r \][/tex]
We need to convert this formula so it uses the diameter [tex]\( d \)[/tex] instead of the radius [tex]\( r \)[/tex]. Let's substitute [tex]\( r \)[/tex] in the circumference formula with [tex]\( \frac{d}{2} \)[/tex].
[tex]\[ C = 2\pi r \][/tex]
[tex]\[ C = 2\pi \left( \frac{d}{2} \right) \][/tex]
Simplify the expression by canceling [tex]\( 2 \)[/tex]:
[tex]\[ C = \pi d \][/tex]
Thus, the equivalent formula for the circumference [tex]\( C \)[/tex] in terms of the diameter [tex]\( d \)[/tex] is:
[tex]\[ C = \pi d \][/tex]
So, the correct answer is:
C. [tex]\( C = \pi d \)[/tex]
