Question

the diameter of a circle is 2 kilometers. what is the area of a sector bounded by an 85° arc? give the exact answer in simplest form. square kilometers

Explanation:

Step1: Calcular radio

Radio \( r = \frac{d}{2} = \frac{2}{2} = 1 \, \text{km} \)

Step2: Aplicar fórmula sector

Área sector \( = \frac{\theta}{360^\circ} \times \pi r^2 = \frac{85^\circ}{360^\circ} \times \pi (1)^2 = \frac{17}{72}\pi \)

Answer:

\(\frac{17}{72}\pi\)