Question

the diameter of a circle is 12 inches. what is the area of a sector bounded by an 84° arc? give the exact answer in simplest form. square inches

Explanation:

Step1: Calculate radius

$r = \frac{12}{2} = 6$ inches

Step2: Area of full circle

$A_{\text{círculo}} = \pi r^2 = \pi (6)^2 = 36\pi$

Step3: Sector fraction

$\text{Fracción} = \frac{84^\circ}{360^\circ} = \frac{7}{30}$

Step4: Sector area

$A_{\text{sector}} = 36\pi \times \frac{7}{30} = \frac{42\pi}{5}$

Answer:

$\frac{42\pi}{5}$ square inches