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?

Question

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1 point
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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.