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To solve the problem, we need to find the area of the sector of a circle with a radius of 9 units and a central angle of 65 degrees.

The formula for the area \( A \) of a sector with a central angle \(\theta\) (in degrees) in a circle of radius \( r \) is:

\[
A = \frac{\theta}{360} \times \pi r^2
\]

### Plugging in the given values:
- \( r = 9 \)
- \(\theta = 65^\circ\)

\[
A = \frac{65}{360} \times \pi \times 9^2
\]

Let's calculate this step-by-step.

First, find the value of \( \pi \times 9^2 \):

\[
9^2 = 81 \quad \Rightarrow \quad \pi \times 81 \approx 254.47
\]

Now multiply by \(\frac{65}{360}\):

\[
A \approx \frac{65}{360} \times 254.47
\]

Now, let me compute the value.The area of the sector is approximately \(45.95\) square units.

Would you like to know more details or have any questions about this solution?

Here are some related questions you might find helpful:
1. How do you convert radians to degrees when calculating the area of a sector?
2. What is the formula for the circumference of a circle, and how is it related to the area of a sector?
3. How would the area change if the radius of the circle was doubled?
4. How do you find the length of an arc corresponding to a given sector angle?
5. What is the significance of the central angle in determining the sector's area?

**Tip:** When working with sectors, always ensure the angle is correctly interpreted in degrees or radians, depending on the formula being used.

Find the area A of the sector shown in the figure, where the central angle is 65° and the radius is 9 units.

Learn how to calculate the area of a sector in a circle with a 65-degree central angle and a radius of 9 units. This problem covers the key geometric concepts of sector area calculations, suitable for students in Grades 9-10.

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