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.
- First, calculate the radius \( r \). The diameter is given as \( 16fy \), so the radius is:
\[ r = \frac{16fy}{2} = 8fy \]
-
The angle \( \theta \) is given as \( \frac{\pi}{2} \) radians.
-
Now, substitute \( r \) and \( \theta \) into the area formula:
\[ \text{Area of sector} = \frac{1}{2} \times (8fy)^2 \times \frac{\pi}{2} \]
- 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
\[ \boxed{16f^2y^2\pi} \]
1 answer