Sure, let's work through the problem step-by-step:
Given:
- The formula for the circumference of a circle is [tex]\( C = 2 \pi r \)[/tex].
- The circumference [tex]\( C \)[/tex] of the circle is 16.
- We are to find the radius [tex]\( r \)[/tex].
First, let's use the given formula solved for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{C}{2 \pi} \][/tex]
We need to substitute the given value of [tex]\( C \)[/tex] into this formula. The given circumference [tex]\( C \)[/tex] is 16.
Substitute [tex]\( C = 16 \)[/tex] into the formula:
[tex]\[ r = \frac{16}{2 \pi} \][/tex]
So, the expression now becomes:
[tex]\[ r = \frac{16}{2 \pi} \][/tex]
Using the value of [tex]\( \pi \approx 3.14159 \)[/tex], let's calculate the radius [tex]\( r \)[/tex]:
[tex]\[ r = \frac{16}{2 \times 3.14159} \][/tex]
Let's simplify the expression in the denominator first:
[tex]\[ 2 \times 3.14159 = 6.28318 \][/tex]
Now, divide 16 by 6.28318:
[tex]\[ r = \frac{16}{6.28318} \approx 2.5464812403910124 \][/tex]
Thus, the radius of the circle is approximately [tex]\( r \approx 2.5464812403910124 \)[/tex].
Let's compare the obtained radius with the options given:
- [tex]\( r - 4 \)[/tex]: Approximately [tex]\( -1.4535187596089876 \)[/tex] (obviously not correct)
- [tex]\( r = 8 \)[/tex]: Incorrect
- [tex]\( r = 12 \)[/tex]: Incorrect
- [tex]\( r = 16 \)[/tex]: Incorrect
Given the correct radius is approximately [tex]\( r \approx 2.5464812403910124 \)[/tex], none of the provided options seem to accurately match the calculated radius.
Therefore, the correct radius for the circle with circumference 16 cannot be found in the provided options. The appropriate value, based on our calculations, is approximately 2.5464812403910124.
