Question
Find area of sector with diameter of 16fy and angle of pie/2 radians
Answers
GPT-4o mini
To find the area of a sector, you can use the formula:
\[
\text{Area} = \frac{1}{2} r^2 \theta
\]
where \( r \) is the radius and \( \theta \) is the angle in radians.
1. **Find the radius**: The diameter is given as \( 16 \, \text{fy} \), so the radius \( r \) is half of the diameter:
\[
r = \frac{16 \, \text{fy}}{2} = 8 \, \text{fy}
\]
2. **Substituting the values**: Now, substitute \( r = 8 \, \text{fy} \) and \( \theta = \frac{\pi}{2} \) into the area formula:
\[
\text{Area} = \frac{1}{2} (8 \, \text{fy})^2 \left(\frac{\pi}{2}\right)
\]
3. **Calculate the area**:
\[
\text{Area} = \frac{1}{2} (64 \, \text{fy}^2) \left(\frac{\pi}{2}\right)
\]
\[
\text{Area} = \frac{64 \pi}{4} \, \text{fy}^2
\]
\[
\text{Area} = 16 \pi \, \text{fy}^2
\]
Therefore, the area of the sector is \( 16 \pi \, \text{fy}^2 \).
\[
\text{Area} = \frac{1}{2} r^2 \theta
\]
where \( r \) is the radius and \( \theta \) is the angle in radians.
1. **Find the radius**: The diameter is given as \( 16 \, \text{fy} \), so the radius \( r \) is half of the diameter:
\[
r = \frac{16 \, \text{fy}}{2} = 8 \, \text{fy}
\]
2. **Substituting the values**: Now, substitute \( r = 8 \, \text{fy} \) and \( \theta = \frac{\pi}{2} \) into the area formula:
\[
\text{Area} = \frac{1}{2} (8 \, \text{fy})^2 \left(\frac{\pi}{2}\right)
\]
3. **Calculate the area**:
\[
\text{Area} = \frac{1}{2} (64 \, \text{fy}^2) \left(\frac{\pi}{2}\right)
\]
\[
\text{Area} = \frac{64 \pi}{4} \, \text{fy}^2
\]
\[
\text{Area} = 16 \pi \, \text{fy}^2
\]
Therefore, the area of the sector is \( 16 \pi \, \text{fy}^2 \).