To find the exact circumference of a circle with a radius of 12 inches, we can use the formula for the circumference of a circle:
[tex]\[ C = 2\pi r \][/tex]
where:
- [tex]\(C\)[/tex] is the circumference,
- [tex]\(\pi\)[/tex] (pi) is a constant approximately equal to 3.14159,
- [tex]\(r\)[/tex] is the radius of the circle.
Given the radius [tex]\(r = 12\)[/tex] inches, we substitute this value into the formula:
[tex]\[ C = 2 \pi \times 12 \][/tex]
[tex]\[ C = 24 \pi \][/tex]
The exact circumference of the circle is [tex]\(24\pi\)[/tex] inches.
We can see that none of the provided choices match exactly as [tex]\(24 \pi\)[/tex] inches. The closest match is:
○ 6π in.
o 12 in.
24 in.
○ 48 in.
None of these options are the correct representation of the exact circumference [tex]\(24 \pi\)[/tex]. Instead, if we were converting [tex]\(24 \pi\)[/tex] inches to its decimal form, it would be approximately [tex]\(24 \times 3.14159 \approx 75.3982\)[/tex] inches, but that is not asked for here. The exact form remains [tex]\(24\pi\)[/tex] inches.
