Question

what is the approximate area of the shaded sector in the circle shown below? 100° a. 15.7 cm² b. 31.4 cm² c. 565 cm² d. 283 cm² 18 cm

Explanation:

Step1: Recall area - of - circle formula

The area of a full - circle is given by $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, $r = 18$ cm, so $A=\pi\times(18)^{2}=324\pi$ $cm^{2}$.

Step2: Find the fraction of the circle represented by the sector

The central angle of the sector is $\theta = 100^{\circ}$, and the total number of degrees in a circle is $360^{\circ}$. The fraction of the circle that the sector represents is $\frac{\theta}{360}=\frac{100}{360}=\frac{5}{18}$.

Step3: Calculate the area of the sector

The area of the sector $A_{s}$ is the fraction of the circle times the area of the full - circle. So $A_{s}=\frac{5}{18}\times324\pi$.
$A_{s}=90\pi$ $cm^{2}$. Using $\pi\approx3.14$, we have $A_{s}\approx90\times3.14 = 282.6\approx283$ $cm^{2}$.

Answer:

D. $283$ $cm^{2}$