Question

the diameter of a circle is 8 miles. what is the angle measure of an arc bounding a sector with area 2π square miles? give the exact answer in simplest form.

Explanation:

Step1: Calcular radio

Radio \( r = \frac{d}{2} = \frac{8}{2} = 4 \) mi

Step2: Fórmula área sector

Área \( K = \frac{\theta}{360^\circ} \cdot \pi r^2 \)

Step3: Sustituir valores

\( 2\pi = \frac{\theta}{360^\circ} \cdot \pi (4)^2 \)

Step4: Simplificar y resolver θ

\( 2\pi = \frac{16\pi \theta}{360^\circ} \Rightarrow \theta = \frac{2 \cdot 360^\circ}{16} = 45^\circ \)

Answer:

45