Annular Sector Area Calculation

Use outer radius and thickness to calculate the arc area

\[arc\, area \\[12pt] = (large\, circle\, area - small\, circle\, area) \times angle\, ratio \\[12pt] = {Pi \, [Outer\, radius^2 - (Outer\, radius - Thickness)^2]} \, {\theta \over 360} \\[12pt] = {Pi \, (2 \cdot outer\, radius \cdot thickness - thickness^2)} \, {\theta \over 360} \\[12pt] = {\pi \, t(2 \cdot OR - t)} \, {\theta \over 360} \]

Use Inner radius, thickness Calculate arc area

\[arc\, area \\[12pt] = (large\, circle\, area - small\, circle\, area) \times angle\, ratio \\[12pt] = {Pi \, [(Inner\, Radius + Thickness)^2 - Inner\, Radius^2]} \, {\theta \over 360} \\[12pt] = {Pi \, (2 \cdot inner\, radius \cdot thickness + thickness^2)} \, {\theta \over 360} \\[12pt] = {\pi \, t(2 \cdot IR + t)} \, {\theta \over 360} \]

Use Outer radius, inner radius Calculate arc area

\[arc\, area \\[12pt] = (large\, circle area - small\, circle area) \times angle\, ratio \\[12pt] = {Pi \, (Outer\, radius^2 - Inner\, radius^2)} \, {\theta \over 360} \\[12pt] = {\pi \, (OR^2 - IR^2)} \, {\theta \over 360} \]