Question

the radius of a circle is 3 miles. what is the area of a sector bounded by a 180° arc? give the exact answer in simplest form. square miles

Explanation:

Step1: Sector area formula

$A = \frac{\theta}{360^\circ} \times \pi r^2$

Step2: Substitute values (θ=180°, r=3)

$A = \frac{180^\circ}{360^\circ} \times \pi (3)^2 = \frac{1}{2} \times 9\pi = \frac{9}{2}\pi$

Answer:

$\frac{9}{2}\pi$ square miles