Question

the diameter of a circle is 8 feet. what is the angle measure of an arc bounding a sector with area 6π square feet? give the exact answer in simplest form.

Explanation:

Step1: Calculate radius

$r = \frac{8}{2} = 4$

Step2: Sector area formula

$6\pi = \frac{\theta}{360} \cdot \pi r^2$

Step3: Substitute $r^2=16$

$6\pi = \frac{\theta}{360} \cdot \pi \cdot 16$

Step4: Cancel $\pi$

$6 = \frac{16\theta}{360}$

Step5: Solve for $\theta$

$\theta = \frac{6 \cdot 360}{16} = 135$

Answer:

135