Question

the radius of a circle is 9 miles. what is the area of a sector bounded by a 120° arc? give the exact answer in simplest form. square miles

Explanation:

Step1: Calculate full circle area

$A_{\text{círculo}} = \pi r^2 = \pi (9)^2 = 81\pi$

Step2: Find sector fraction

$\text{Fracción} = \frac{120^\circ}{360^\circ} = \frac{1}{3}$

Step3: Compute sector area

$A_{\text{sector}} = \text{Fracción} \times A_{\text{círculo}} = \frac{1}{3} \times 81\pi = 27\pi$

Answer:

27π square miles