Question

the diameter of a circle is 18 inches. what is the area of a sector bounded by a 40° arc? give the exact answer in simplest form. square inches

Explanation:

Step1: Calculate radius

$r = \frac{18}{2} = 9$ inches

Step2: Area of full circle

$A_{\text{círculo}} = \pi r^2 = \pi (9)^2 = 81\pi$

Step3: Sector area fraction

$\text{Fracción} = \frac{40^\circ}{360^\circ} = \frac{1}{9}$

Step4: Sector area

$A_{\text{sector}} = \frac{1}{9} \times 81\pi = 9\pi$

Answer:

$9\pi$ square inches