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We are given that the area of a sector is 126.4 cm², and the subtended angle is 104°. We are asked to find the radius of the circle.

The formula for the area of a sector is:

\[
A = \frac{\theta}{360} \times \pi r^2
\]

Where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle of the sector (in degrees),
- \( r \) is the radius of the circle.

Given:
\[
A = 126.4 \, \text{cm}^2, \quad \theta = 104^\circ
\]

Now, let's solve for the radius \( r \).

First, rearrange the formula to solve for \( r \):

\[
r^2 = \frac{A \times 360}{\theta \times \pi}
\]
\[
r = \sqrt{\frac{A \times 360}{\theta \times \pi}}
\]

Let me calculate that for you.It seems there was a technical issue with the calculation tool. However, I can guide you through solving this manually:

We are using the formula:

\[
r = \sqrt{\frac{A \times 360}{\theta \times \pi}}
\]

Substitute the values:

\[
r = \sqrt{\frac{126.4 \times 360}{104 \times \pi}}
\]

First, calculate the numerator and denominator:

\[
126.4 \times 360 = 45,504
\]
\[
104 \times \pi \approx 326.7256
\]

Now divide the results:

\[
\frac{45,504}{326.7256} \approx 139.26
\]

Finally, take the square root:

\[
r \approx \sqrt{139.26} \approx 11.8 \, \text{cm}
\]

Thus, the radius is approximately \( 11.8 \, \text{cm} \), which matches the given solution. 

Would you like further clarification or details on any step?

Here are 5 related questions to consider:
1. How would the radius change if the subtended angle were doubled?
2. What is the formula for the circumference of a circle, and how does the radius relate to it?
3. How can you find the length of the arc in this sector problem?
4. What is the relationship between the area of a circle and its radius?
5. How would this problem change if the area of the sector were given in square meters?

**Tip**: When dealing with circle sectors, always remember that the subtended angle affects only a fraction of the entire circle's area.

A sector of a circle has an area of 126.4 cm² and a subtended angle of 104°. What is its radius?

Learn how to calculate the radius of a circle sector with an area of 126.4 cm² and a subtended angle of 104°. This problem applies geometric formulas and involves solving for the radius. Suitable for Grades 8-10.

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