Question

question 11 of 25. to the nearest square inch, what is the area of the shaded sector in the circle shown below? 10 in 133°. a. 23 in² b. 314 in² c. 464 in² d. 116 in²

Explanation:

Step1: Recall area - of - sector formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central angle of the sector and $r$ is the radius of the circle.

Step2: Identify given values

We are given that $\theta = 133^{\circ}$ and $r = 10$ inches.

Step3: Substitute values into formula

$A=\frac{133}{360}\times\pi\times(10)^{2}=\frac{133}{360}\times100\pi=\frac{13300\pi}{360}=\frac{665\pi}{18}$.

Step4: Calculate the value

Using $\pi\approx3.14$, we have $A=\frac{665\times3.14}{18}=\frac{2088.1}{18}\approx116$ in².

Answer:

D. 116 in²