Question

Find area of sector with diameter of 16fy 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 formula:

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

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

1. First, calculate the radius \( r \). The diameter is given as \( 16fy \), so the radius is:

\[
r = \frac{16fy}{2} = 8fy
\]

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

3. Now, substitute \( r \) and \( \theta \) into the area formula:

\[
\text{Area of sector} = \frac{1}{2} \times (8fy)^2 \times \frac{\pi}{2}
\]

4. Simplify this expression:

\[
= \frac{1}{2} \times 64f^2y^2 \times \frac{\pi}{2}
\]
\[
= \frac{64f^2y^2 \pi}{4}
\]
\[
= 16f^2y^2\pi
\]

So, the area of the sector is

\[
\boxed{16f^2y^2\pi}
\]