Sector Area Math Example 4

Solution

1. 1
   Step 1: Full sector area (radius 15 ft, 120°): $A_{\text{full}} = \frac{120}{360} \times \pi(15)^2 = \frac{1}{3} \times 225\pi = 75\pi \approx 235.6$ ft².
2. 2
   Step 2: Inner sector area (radius 10 ft, 120°): $A_{\text{inner}} = \frac{120}{360} \times \pi(10)^2 = \frac{1}{3} \times 100\pi = \frac{100\pi}{3} \approx 104.7$ ft².
3. 3
   Step 3: Annular sector area $= A_{\text{full}} - A_{\text{inner}} = 75\pi - \frac{100\pi}{3} = \frac{225\pi - 100\pi}{3} = \frac{125\pi}{3} \approx 130.9$ ft².