https://file.aiquickdraw.com/mathbot/file/172540970314860rn67fg.jpg

To solve the problem, we need to calculate the area of a sector of a circle given the central angle and the radius.

### Formula:
The area \( A \) of a sector with a central angle \( \theta \) (in degrees) and radius \( r \) is given by:

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

### Given Values:
- Central angle \( \theta = 246^\circ \)
- Radius \( r = 7.8 \) mm

### Calculation:
1. **Compute the area using the formula**:
   \[
   A = \frac{246^\circ}{360^\circ} \times \pi \times (7.8)^2
   \]
2. **Simplify the expression**:
   \[
   A = \frac{246}{360} \times \pi \times 60.84
   \]

3. **Use the approximate value for \( \pi \) as \( 3.1416 \)** since the problem specifies not to use the symbol \( \pi \):
   \[
   A = \frac{246}{360} \times 3.1416 \times 60.84
   \]

Now, let's calculate this step by step.

I'll proceed with the calculation.The area of the sector is approximately **130.6089 square millimeters** when rounded to four decimal places.

Would you like any additional details or have any questions?

Here are some related questions you might find interesting:
1. How does the area change if the central angle is increased to 300°?
2. What is the area of a full circle with the given radius?
3. How would the formula change if the angle were given in radians?
4. How does the area of the sector compare to the total area of the circle?
5. What if the radius was doubled? How would the area of the sector be affected?

**Tip:** Always ensure to use the correct value for \( \pi \) as specified in a problem, especially when an approximation is required.

Find the area of a sector with a central angle of 246° in a circle of radius 7.8 mm.

Learn how to calculate the area of a sector with a central angle of 246° in a circle with a radius of 7.8 mm. This geometry problem involves using the sector area formula and is suitable for high school students in Grades 9-12.

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