what is the area of sector gph?\nthe area of sector gph is $\\square$ square yards.\n(type an exact answer…
what is the area of sector gph?\nthe area of sector gph is $\\square$ square yards.\n(type an exact answer in terms of $\\pi$.)
Answer
Explanation:
Step1: Identify the radius and central angle
The radius $r$ is $9\text{ yd}$ and the central angle $\theta$ is $80^{\circ}$.
Step2: State the sector area formula
$$A = \frac{\theta}{360^{\circ}} \cdot \pi r^2$$
Step3: Substitute the given values
$$A = \frac{80^{\circ}}{360^{\circ}} \cdot \pi \cdot (9)^2$$
Step4: Simplify the fraction and square
$$A = \frac{2}{9} \cdot \pi \cdot 81$$
Step5: Calculate the final area
$$A = 2 \cdot \pi \cdot 9 = 18\pi$$
Answer:
$18\pi$