using the radiujs of 30 meters and the central angle of 36 degreess. Give me the area of the sector in terms of pi, and in decimal form

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

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

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

Given:
- \(r = 30\) meters
- \(\theta = 36^\circ\)

### Step 1: Substitute the values into the formula.

\[
\text{Area of Sector} = \frac{36^\circ}{360^\circ} \times \pi \times (30)^2
\]

### Step 2: Simplify the expression.

\[
\text{Area of Sector} = \frac{1}{10} \times \pi \times 900 = 90\pi \text{ square meters}
\]

### Step 3: Convert to decimal form.

\[
\text{Area of Sector} \approx 90 \times 3.14159 = 282.74 \text{ square meters}
\]

### Final Answer:
- In terms of \(\pi\): \(90\pi\) square meters
- In decimal form: \(282.74\) square meters

Would you like further details on this process, or do you have any other questions?

Here are some related questions:
1. How do you find the length of the arc of a sector?
2. What would be the area if the central angle was doubled?
3. How does the area change if the radius is halved?
4. What is the full circle area with a radius of 30 meters?
5. How do you find the perimeter of the sector?

**Tip:** Remember, the sector area is always a fraction of the full circle's area, proportional to the angle of the sector.

Learn how to calculate the area of a sector of a circle with a radius of 30 meters and a central angle of 36 degrees. Step-by-step solution provided in terms of pi and decimal form. Suitable for high school students studying geometry.

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