The circle shown with radius   has a sector with a central angle of  . What is the area of the sector?

To find the area of the sector of a circle given its radius and central angle, we can follow these steps:

1. Break Down the Problem

• Identify the radius of the circle $r$.
• Identify the central angle of the sector $\theta$ in degrees (or radians if specified).
• Find the area of the sector using the formula.

2. Relevant Concepts

The formula to find the area $A$ of a sector of a circle is given by:

$A = \frac{\theta}{360} \times \pi r^2 \quad \text{(if } \theta \text{ is in degrees)}$ or $A = \frac{1}{2} r^2 \theta \quad \text{(if } \theta \text{ is in radians)}$

3. Analysis and Detail

1. Convert the angle: If the angle is provided in degrees, use the first formula. If in radians, then use the second formula.
2. Plug in the values: Replace $\theta$ and $r$ in the chosen formula to calculate the area.

4. Verify and Summarize

• Ensure the units are consistent (i.e., radius in the same unit).
• Multiply correctly and check that you have used the right formula based on the angle measurement.

Final Answer

Once values for $r$ and $\theta$ have been provided, substitute them into the appropriate formula to find the area of the sector to get your final answer.

If you provide the specific values for the radius and angle, I can give you a numerical result.