Question

Can you please help me

Answer 1

To obtain the area of the shaded sector, the following steps are necessary:

Step 1: Recall the formula for the area of a sector, as below:

$A_{\sec tor}=\frac{\theta}{360}\times\pi\times r^2$

Where:

$\begin{gathered} \theta=\sec tor\text{ angle} \\ r=\text{radius of circle} \\ \pi=3.142.. \end{gathered}$

Step 2: Apply the formula to obtain the area of the shaded sector in the question, as follows:

$\begin{gathered} A_{\sec tor}=\frac{\theta}{360}\times\pi\times r^2 \\ \sin ce\colon\text{ }\theta=36^o,\text{ and r= 6 in, we have:} \\ A_{\sec tor}=\frac{36}{360}\times\pi\times6^2 \\ \Rightarrow A_{\sec tor}=\frac{36}{360}\times3.142\times36 \\ \Rightarrow A_{\sec tor}=\frac{4072.032}{360}=11.31in^2 \\ \Rightarrow A_{\sec tor}=11.31in^2 \end{gathered}$

Therefore, the area of the shaded sector is 11.31 square inches (option B)