To determine the area of a [tex]\(45^\circ\)[/tex] sector of a circle with an area of [tex]\(24 \, m^2\)[/tex], follow these steps:
1. Understand the problem:
- You need to find the area of a sector.
- The total area of the circle is [tex]\(24 \, m^2\)[/tex].
- The angle of the sector is [tex]\(45^\circ\)[/tex].
2. Recall the formula for the area of a sector:
[tex]\[
\text{Area of a sector} = \left( \frac{\theta}{360^\circ} \right) \times \text{Area of the circle}
\][/tex]
where [tex]\(\theta\)[/tex] is the angle of the sector.
3. Substitute the given values into the formula:
[tex]\[
\text{Area of the sector} = \left( \frac{45^\circ}{360^\circ} \right) \times 24 \, m^2
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{45^\circ}{360^\circ} = \frac{1}{8}
\][/tex]
5. Calculate the area of the sector:
[tex]\[
\text{Area of the sector} = \left( \frac{1}{8} \right) \times 24 \, m^2 = 3 \, m^2
\][/tex]
Therefore, the area of the [tex]\(45^\circ\)[/tex] sector is [tex]\(3 \, m^2\)[/tex].
The correct answer is:
C. [tex]\(3 \, m^2\)[/tex]
