Question
The radius of a circle is 6 in. Find the area of a sector with an angle of 120°.(1 point)
Responses
A=2π in.2
upper A equals 2 pi in. squared
A=36π in.2
upper A equals 36 pi in. squared
A=12π in.2
upper A equals 12 pi in. squared
A=9π in.2
Responses
A=2π in.2
upper A equals 2 pi in. squared
A=36π in.2
upper A equals 36 pi in. squared
A=12π in.2
upper A equals 12 pi in. squared
A=9π in.2
Answers
GPT-4o mini
To find the area of a sector with a given angle in a circle, you can use the formula:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle of the sector in degrees,
- \( r \) is the radius of the circle.
In this case, the radius \( r \) is 6 inches and the angle \( \theta \) is 120°.
1. Calculate the area of the entire circle using the radius:
\[
A_{\text{circle}} = \pi r^2 = \pi (6^2) = \pi \times 36 = 36\pi \text{ in}^2
\]
2. Now apply the sector formula:
\[
A = \frac{120}{360} \times 36\pi = \frac{1}{3} \times 36\pi = 12\pi \text{ in}^2
\]
Thus, the area of the sector is \( A = 12\pi \text{ in}^2 \).
The correct response is:
**A = 12π in.²**
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle of the sector in degrees,
- \( r \) is the radius of the circle.
In this case, the radius \( r \) is 6 inches and the angle \( \theta \) is 120°.
1. Calculate the area of the entire circle using the radius:
\[
A_{\text{circle}} = \pi r^2 = \pi (6^2) = \pi \times 36 = 36\pi \text{ in}^2
\]
2. Now apply the sector formula:
\[
A = \frac{120}{360} \times 36\pi = \frac{1}{3} \times 36\pi = 12\pi \text{ in}^2
\]
Thus, the area of the sector is \( A = 12\pi \text{ in}^2 \).
The correct response is:
**A = 12π in.²**