To find the circumference and the area of a circle with a radius of 2 inches, we can use the following formulas:
Circumference:
[tex]\[ C = 2 \pi r \][/tex]
Area:
[tex]\[ A = \pi r^2 \][/tex]
Given:
[tex]\[ r = 2 \, \text{inches} \][/tex]
1. Calculate the Circumference:
- First, substitute the radius (2 inches) into the circumference formula:
[tex]\[ C = 2 \pi \times 2 \][/tex]
- Simplifying further:
[tex]\[ C = 4 \pi \][/tex]
- Using the value of [tex]\(\pi \approx 3.14159\)[/tex], the circumference can be approximated:
[tex]\[ C \approx 4 \times 3.14159 \approx 12.56636 \][/tex]
- Rounding this result to the nearest tenth:
[tex]\[ \boxed{12.6} \][/tex]
2. Calculate the Area:
- Substitute the radius (2 inches) into the area formula:
[tex]\[ A = \pi \times (2)^2 \][/tex]
- Simplifying further:
[tex]\[ A = \pi \times 4 \][/tex]
- Using the value of [tex]\(\pi \approx 3.14159\)[/tex], the area can be approximated:
[tex]\[ A \approx 4 \times 3.14159 \approx 12.56636 \][/tex]
- Rounding this result to the nearest tenth:
[tex]\[ \boxed{12.6} \][/tex]
Therefore, the circumference of the circle is [tex]\(12.6\)[/tex] inches, and the area of the circle is [tex]\(12.6\)[/tex] square inches.
