Question

question 2 of 10 what is the approximate area of the shaded sector in the circle shown below? 100° 16 cm c a. 31.4 cm² b. 15.7 cm² c. 283 cm² d. 565 cm²

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, 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 $\theta = 100^{\circ}$ and $r = 18\ cm$.

Step3: Substitute values into the formula

$A=\frac{100^{\circ}}{360^{\circ}}\times\pi\times(18)^{2}$.
First, calculate $(18)^{2}=324$. Then, $\frac{100}{360}\times\pi\times324=\frac{100\times324\pi}{360}$.
Simplify $\frac{100\times324}{360}=\frac{32400}{360}=90$. So, $A = 90\pi$.

Step4: Approximate the value

Take $\pi\approx3.14$. Then $A\approx90\times3.14 = 282.6\approx283\ cm^{2}$.

Answer:

C. $283\ cm^{2}$