A sector of a circle has a central angle of 155°. Find the area of the sector if the radius of the circle is 7 ft. (Round your answer to one decimal place.)

To find the area of the sector of a circle, you can use the 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:
- \(\theta = 155^\circ\)
- \(r = 7\) ft

Now, substitute the values into the formula:

\[
\text{Area of the sector} = \frac{155^\circ}{360^\circ} \times \pi \times (7)^2
\]

\[
\text{Area of the sector} = \frac{155}{360} \times \pi \times 49
\]

\[
\text{Area of the sector} = \frac{155 \times 49 \times \pi}{360}
\]

Let's calculate this.

\[
\text{Area of the sector} \approx \frac{7595 \times \pi}{360} \approx 66.1 \text{ square feet}
\]

So, the area of the sector is approximately **66.1 square feet**.

Would you like any more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the area of the sector change if the central angle was reduced to 90°?
2. What would be the area of a sector with the same radius but a central angle of 210°?
3. How do you calculate the circumference of a circle with the same radius?
4. What is the area of the entire circle with the given radius?
5. How does changing the radius affect the area of the sector for a fixed central angle?

**Tip:** When working with sectors, always ensure that your angle is in degrees if you're using the standard sector area formula, or convert to radians if needed.

Learn how to calculate the area of a sector of a circle with a 155° central angle and a radius of 7 ft using the sector area formula. This problem involves basic geometry concepts and requires knowledge of the circle sector formula. Suitable for high school students.

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