Sector Area Math Example 2

Solution

1. 1
   Step 1: Use the radian sector area formula: $A = \frac{1}{2}r^2\theta$.
2. 2
   Step 2: Substitute $r = 9$ cm and $\theta = \frac{2\pi}{3}$: $A = \frac{1}{2}(9)^2 \cdot \frac{2\pi}{3}$.
3. 3
   Step 3: Compute $r^2 = 81$, then $A = \frac{1}{2} \times 81 \times \frac{2\pi}{3}$.
4. 4
   Step 4: Simplify: $A = \frac{81 \times 2\pi}{6} = \frac{162\pi}{6} = 27\pi \approx 84.82$ cm².