Question

28 find the area of the sector of the circle pictured below. (you should write the formula for area of a sector on you
work:
answer with π :
answer rounded to tenths:
notes: area of a sector = π r² (angle)/360

Explanation:

Step1: Identify given values

Radius \( r = 18 \) ft, angle \( \theta = 145^\circ \). Formula: \( A=\pi r^{2}\frac{\theta}{360} \)

Step2: Substitute values into formula

\( A = \pi\times18^{2}\times\frac{145}{360} \)
Calculate \( 18^{2}=324 \), so \( A=\pi\times324\times\frac{145}{360} \)
Simplify \( \frac{324\times145}{360}=\frac{324}{360}\times145 = 0.9\times145 = 130.5 \), so \( A = 130.5\pi \) (for answer with \( \pi \))

Step3: Calculate numerical value (rounded to tenths)

\( 130.5\pi\approx130.5\times3.1416\approx410.0 \) (rounded to tenths)

Work:

\( A=\pi\times18^{2}\times\frac{145}{360}=\pi\times324\times\frac{145}{360}=130.5\pi \)

Answer:

with \( \pi \):
\( 130.5\pi \) square feet