Question

If the area of a circle is 36 square meters, and the measure of a sector within that circle is 120°, what is the area of that sector?

Answer 1

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

\[
\text{Area of sector} = \left(\frac{\theta}{360}\right) \times \text{Area of circle}
\]

where \(\theta\) is the angle of the sector in degrees.

1. **Given**: The area of the circle is \(36\) square meters, and the angle of the sector is \(120^\circ\).

2. **Substitute the values into the formula**:

\[
\text{Area of sector} = \left(\frac{120}{360}\right) \times 36
\]

3. **Calculate \(\frac{120}{360}\)**:

\[
\frac{120}{360} = \frac{1}{3}
\]

4. **Now substitute this back into the area formula**:

\[
\text{Area of sector} = \frac{1}{3} \times 36
\]

5. **Calculate the area**:

\[
\text{Area of sector} = 12 \text{ square meters}
\]

Thus, the area of the sector is \( \boxed{12} \) square meters.