Question

Find area of sector with diameter of 16ft and angle of pie over 2 radians

Answer 1

To find the area of a sector given the diameter and the angle in radians, you can use the following formula for the area of a sector:

\[
\text{Area} = \frac{1}{2} r^2 \theta
\]

where \( r \) is the radius and \( \theta \) is the angle in radians.

1. First, calculate the radius:
- The diameter is given as 16 ft, so the radius \( r \) is:
\[
r = \frac{\text{diameter}}{2} = \frac{16 \text{ ft}}{2} = 8 \text{ ft}
\]

2. The angle \( \theta \) is given as \( \frac{\pi}{2} \) radians.

3. Now, plug \( r \) and \( \theta \) into the area formula:
\[
\text{Area} = \frac{1}{2} \times (8 \text{ ft})^2 \times \frac{\pi}{2}
\]
\[
= \frac{1}{2} \times 64 \text{ ft}^2 \times \frac{\pi}{2}
\]
\[
= \frac{64 \text{ ft}^2 \cdot \pi}{4}
\]
\[
= 16\pi \text{ ft}^2
\]

Thus, the area of the sector is \( 16\pi \text{ ft}^2 \).

If you need a numerical approximation, you can calculate \( 16\pi \approx 16 \times 3.14 = 50.24 \text{ ft}^2 \).

So, the area of the sector is approximately \( 50.24 \text{ ft}^2 \).