A sector with a central angle of 288 degrees is carved out of a circle with a radius of 6cm. What is the area, in cm2, of the sector? 

To find the area of a sector, we use the formula:

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

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

Given:
- \(\theta = 288^\circ\)
- \(r = 6 \, \text{cm}\)

Substituting these values into the formula:

\[
\text{Area of the sector} = \frac{288}{360} \times \pi \times 6^2
\]

Now, let's calculate it step by step:

1. Simplify the fraction: 

   \[
   \frac{288}{360} = \frac{4}{5}
   \]

2. Calculate \(6^2\):

   \[
   6^2 = 36
   \]

3. Substitute and simplify:

   \[
   \text{Area of the sector} = \frac{4}{5} \times \pi \times 36 = \frac{4 \times 36 \times \pi}{5}
   \]

4. Calculate the value:

   \[
   \text{Area of the sector} = \frac{144\pi}{5} \approx 90.48 \, \text{cm}^2
   \]

Therefore, the area of the sector is approximately:

\[
\boxed{90.48 \, \text{cm}^2}
\]

Would you like a further breakdown of the steps, or do you have any questions?

Here are some related questions that expand on this topic:
1. How do you find the perimeter of a sector with a given radius and central angle?
2. What is the relationship between the area of a sector and the area of the full circle?
3. How do you calculate the arc length of a sector?
4. How does changing the radius affect the area of the sector?
5. How would the area change if the central angle were halved?

**Tip:** Always ensure the angle is in degrees when using this sector area formula, or convert if given in radians!

Discover how to calculate the area of a circle sector with a central angle of 288 degrees and a radius of 6cm. Use the formula for the area of a sector and follow a step-by-step solution. Ideal for students and learners interested in geometry and circle calculations.

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