Question

the radius of a circle is 15 kilometers. what is the area of a sector bounded by an 80° arc? give the exact answer in simplest form. square kilometers

Explanation:

Step1: Calculate r²

$15^2 = 225$

Step2: Compute circle area

$\pi r^2 = 225\pi$

Step3: Find sector fraction

$\frac{80^\circ}{360^\circ} = \frac{2}{9}$

Step4: Sector area = fraction × circle area

$\frac{2}{9} \times 225\pi = 50\pi$

Answer:

$50\pi$