To determine the diameter of a circle given its circumference, we start with the basic relationship between the circumference [tex]\( C \)[/tex] and the diameter [tex]\( d \)[/tex] of a circle. This relationship is given by the formula:
[tex]\[ C = \pi \times d \][/tex]
We are given the circumference [tex]\( C \)[/tex] as 5 units. Thus, we can substitute this value into the equation to solve for [tex]\( d \)[/tex]:
[tex]\[ 5 = \pi \times d \][/tex]
To isolate [tex]\( d \)[/tex], we divide both sides of the equation by [tex]\( \pi \)[/tex]:
[tex]\[ d = \frac{5}{\pi} \][/tex]
So the diameter of the circle is [tex]\(\frac{5}{\pi}\)[/tex].
Next, we compare this result with the given options:
1. [tex]\(\frac{2.5}{\pi^2}\)[/tex]
2. [tex]\(\frac{2.5}{\pi}\)[/tex]
3. [tex]\(\frac{5}{\pi^2}\)[/tex]
4. [tex]\(\frac{5}{\pi}\)[/tex]
From the calculation, we see that the diameter [tex]\( d \)[/tex] matches option 4:
[tex]\[
d = \frac{5}{\pi}
\][/tex]
Thus, the correct answer is:
4) [tex]\(\frac{5}{\pi}\)[/tex]
