Question

the radius of a circle is 8 kilometers. what is the area of a sector bounded by a 90° arc? give the exact answer in simplest form. square kilometers

Explanation:

Step1: Área del círculo completo

$A_{\text{círculo}} = \pi r^2 = \pi (8)^2 = 64\pi \, \text{km}^2$

Step2: Fracción del sector

$\text{Fracción} = \frac{90^\circ}{360^\circ} = \frac{1}{4}$

Step3: Área del sector

$A_{\text{sector}} = 64\pi \times \frac{1}{4} = 16\pi \, \text{km}^2$

Answer:

16π square kilometers