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?
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1 point
Captionless Image
36 square meters
12 square meters
18 square meters
20 square meters

Answer 1

To find the area of a sector of a circle, you 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.

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

Now, replacing the values in the formula:

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

Calculating \(\frac{120}{360}\):

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

Now, substituting this back:

\[
\text{Area of sector} = \left(\frac{1}{3}\right) \times 36 = 12 \text{ square meters}
\]

So, the area of the sector is **12 square meters**.