Question
Identify the circumference and area of the given circle use the formula sheet. The radius is 11 inches. What is the circumference and area of the circle?
Answers
Answered by
GPT-4o mini
To find the circumference and area of a circle, you can use the following formulas:
1. **Circumference (C)**: \( C = 2\pi r \)
2. **Area (A)**: \( A = \pi r^2 \)
Where \( r \) is the radius of the circle.
Given that the radius \( r = 11 \) inches:
1. **Circumference**:
\[
C = 2\pi(11) = 22\pi \text{ inches}
\]
Approximating \( \pi \) as 3.14:
\[
C \approx 22 \times 3.14 \approx 69.08 \text{ inches}
\]
2. **Area**:
\[
A = \pi(11^2) = \pi(121) = 121\pi \text{ square inches}
\]
Approximating \( \pi \) as 3.14:
\[
A \approx 121 \times 3.14 \approx 379.94 \text{ square inches}
\]
Therefore, the circumference of the circle is \( 22\pi \) inches (approximately 69.08 inches), and the area of the circle is \( 121\pi \) square inches (approximately 379.94 square inches).
1. **Circumference (C)**: \( C = 2\pi r \)
2. **Area (A)**: \( A = \pi r^2 \)
Where \( r \) is the radius of the circle.
Given that the radius \( r = 11 \) inches:
1. **Circumference**:
\[
C = 2\pi(11) = 22\pi \text{ inches}
\]
Approximating \( \pi \) as 3.14:
\[
C \approx 22 \times 3.14 \approx 69.08 \text{ inches}
\]
2. **Area**:
\[
A = \pi(11^2) = \pi(121) = 121\pi \text{ square inches}
\]
Approximating \( \pi \) as 3.14:
\[
A \approx 121 \times 3.14 \approx 379.94 \text{ square inches}
\]
Therefore, the circumference of the circle is \( 22\pi \) inches (approximately 69.08 inches), and the area of the circle is \( 121\pi \) square inches (approximately 379.94 square inches).