Find the area of a sector of a circle having radius r and central angle theta.
requals11.2 ​cm, thetaequals66degrees
Question content area bottom
Part 1
The area is approximately 
  
enter your response here cmsquared. 

To find the area of a sector of a circle, you can use the following formula:

\[
\text{Area of the sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta\) is the central angle in degrees.
- \(r\) is the radius of the circle.

Given:
- \(r = 11.2 \, \text{cm}\)
- \(\theta = 66^\circ\)

Substitute the values into the formula:

\[
\text{Area} = \frac{66^\circ}{360^\circ} \times \pi \times (11.2 \, \text{cm})^2
\]

Now, let's calculate it:

\[
\text{Area} = \frac{66}{360} \times \pi \times 11.2^2
\]

\[
\text{Area} = \frac{66}{360} \times \pi \times 125.44 \, \text{cm}^2
\]

\[
\text{Area} \approx 0.1833 \times 3.1416 \times 125.44 \, \text{cm}^2
\]

\[
\text{Area} \approx 72.21 \, \text{cm}^2
\]

So, the area of the sector is approximately **72.21 cm²**.

Would you like more details or have any questions? Here are some related questions:

1. How does the area of a sector change if the central angle is doubled?
2. What is the area of a sector if the radius is halved but the angle remains the same?
3. How would the formula change if the angle was given in radians instead of degrees?
4. What is the relationship between the area of a sector and the circumference of the circle?
5. How can you derive the formula for the area of a sector from the area of a full circle?

**Tip:** Always ensure that the angle is in degrees when using this formula unless specifically asked to work in radians.

Learn how to calculate the area of a sector of a circle with a radius of 11.2 cm and a central angle of 66 degrees using the area formula. Detailed step-by-step solution provided.

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