Question

to the nearest square centimeter, what is the area of the shaded sector in the circle shown below? 12 cm 110° a. 138 cm² b. 151 cm² c. 12 cm² d. 23 cm²

Explanation:

Step1: Recall sector - area 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 values of $\theta$ and $r$

Given that $r = 12$ cm and $\theta=110^{\circ}$.

Step3: Substitute values into the formula

$A=\frac{110}{360}\times\pi\times(12)^{2}$. First, calculate $(12)^{2}=144$. Then, $\frac{110}{360}\times144\times\pi=\frac{110\times144}{360}\times\pi$. $110\times144 = 15840$ and $\frac{15840}{360}=44$. So, $A = 44\pi$.

Step4: Approximate the value

Using $\pi\approx3.14$, we have $A\approx44\times3.14 = 138.16\approx138$ $cm^{2}$.

Answer:

A. $138$ $cm^{2}$