Question

the diameter of a circle is 10 miles. what is the angle measure of an arc bounding a sector with area 10π square miles?
k = 10π sq. mi
d = 10 mi
give the exact answer in simplest form.

Explanation:

Step1: Calculate radius

$r = \frac{d}{2} = \frac{10}{2} = 5$ miles

Step2: Sector area formula

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

Step3: Substitute values

$10\pi = \frac{\theta}{360^\circ} \cdot \pi (5)^2$

Step4: Simplify and solve for θ

$\theta = \frac{10\pi \cdot 360^\circ}{\pi \cdot 25} = 144^\circ$

Answer:

144