Let's solve this problem step by step.
1. Circumference of Circle L:
- The circumference [tex]\(C\)[/tex] of a circle with radius [tex]\(r\)[/tex] is given by the formula:
[tex]\[
C = 2 \pi r
\][/tex]
- Given [tex]\(r = 5\)[/tex] units, the circumference of circle [tex]\(L\)[/tex] is:
[tex]\[
C = 2 \pi \times 5 = 10 \pi \approx 31.4159 \text{ units}
\][/tex]
2. Area of Circle L:
- The area [tex]\(A\)[/tex] of a circle with radius [tex]\(r\)[/tex] is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
- Given [tex]\(r = 5\)[/tex] units, the area of circle [tex]\(L\)[/tex] is:
[tex]\[
A = \pi \times 5^2 = 25 \pi \approx 78.5398 \text{ square units}
\][/tex]
3. [tex]\(\frac{1}{8}\)[/tex] the Circumference:
- To find [tex]\(\frac{1}{8}\)[/tex] of the circumference:
[tex]\[
\frac{1}{8} \times 10 \pi \approx 3.92699 \text{ units}
\][/tex]
4. [tex]\(\frac{1}{8}\)[/tex] the Area:
- To find [tex]\(\frac{1}{8}\)[/tex] of the area:
[tex]\[
\frac{1}{8} \times 25 \pi \approx 9.81748 \text{ square units}
\][/tex]
5. [tex]\(\frac{1}{2}\)[/tex] the Circumference:
- To find [tex]\(\frac{1}{2}\)[/tex] of the circumference:
[tex]\[
\frac{1}{2} \times 10 \pi \approx 15.70796 \text{ units}
\][/tex]
6. [tex]\(\frac{1}{2}\)[/tex] the Area:
- To find [tex]\(\frac{1}{2}\)[/tex] of the area:
[tex]\[
\frac{1}{2} \times 25 \pi \approx 39.2699 \text{ square units}
\][/tex]
Thus, the statements best describing the following are:
- [tex]\(\frac{1}{8}\)[/tex] the circumference of circle L: approximately [tex]\(3.927\)[/tex] units.
- [tex]\(\frac{1}{8}\)[/tex] the area of circle L: approximately [tex]\(9.817\)[/tex] square units.
- [tex]\(\frac{1}{2}\)[/tex] the circumference of circle L: approximately [tex]\(15.708\)[/tex] units.
- [tex]\(\frac{1}{2}\)[/tex] the area of circle L: approximately [tex]\(39.27\)[/tex] square units.
