Question

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

Answer 1

`A_(\sec tor)=45.216in^2`

Step-by-step 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} (64)/(360)=(A_(\sec tor))/(A_(circle))\rightarrow(64)/(360)=(A_(\sec tor))/(254.31) \\ \therefore\rightarrow \\ A_(\sec tor)=(254.31*64)/(360)=(16,277.76)/(360)=45.216in^2 \\ A_(\sec tor)=45.216in^2 \end{gathered}`