Question

the radius of a circle is 8 centimeters. what is the angle measure of an arc bounding a sector with area 8π square centimeters? k = 8π sq. cm r = 8 cm give the exact answer in simplest form.

Explanation:

Step1: Sector area formula

$K = \frac{\theta}{360^\circ} \cdot \pi r^2$

Step2: Substitute known values

$8\pi = \frac{\theta}{360^\circ} \cdot \pi \cdot 8^2$

Step3: Simplify equation

$8 = \frac{64\theta}{360^\circ}$

Step4: Solve for θ

$\theta = \frac{8 \cdot 360^\circ}{64} = 45^\circ$

Answer:

45