Question

the diameter of a circle is 16 feet. what is the angle measure of an arc bounding a sector with area 18π square feet? k = 18π sq. ft d = 16 ft give the exact answer in simplest form.

Explanation:

Step1: Calculate radius

Radius \( r = \frac{d}{2} = \frac{16}{2} = 8 \) ft.

Step2: Sector area formula

\( K = \frac{\theta}{360^\circ} \cdot \pi r^2 \), donde \( K = 18\pi \).

Step3: Substitute values

\( 18\pi = \frac{\theta}{360^\circ} \cdot \pi (8)^2 \).

Step4: Simplify and solve for θ

Cancel \( \pi \): \( 18 = \frac{\theta}{360^\circ} \cdot 64 \).
\( \theta = \frac{18 \cdot 360^\circ}{64} = 101.25^\circ \).

Answer:

101.25