Question

Question 3 Find the Area 64 G H r = 9 in

Answer 1

Answer:

$A_{\sec tor}=45.216in^2$

Explanation: We need to find the area of the shaded sector that has an angle of 64 degrees:

We can reason that it must be the portion of the total area of the circle, and we also know the radius of the circle:

The area of the circle is:

$A_{circle}=\pi r^2=\pi(9in)^2=81\pi=254.31in^2$

The area of the sector is:

We know that 64 degrees are part of the full circle which is 360 degrees, therefore:

$\begin{gathered} \frac{64}{360}=\frac{A_{\sec tor}}{A_{circle}}\rightarrow\frac{64}{360}=\frac{A_{\sec tor}}{254.31} \\ \therefore\rightarrow \\ A_{\sec tor}=\frac{254.31\times64}{360}=\frac{16,277.76}{360}=45.216in^2 \\ A_{\sec tor}=45.216in^2 \end{gathered}$