Question

question 8 of 10

a circle has an area of \\(36\text{ m}^2\\). what is the area of a \\(40^\circ\\) sector of this circle?

a. \\(6\text{ m}^2\\)
b. \\(2\text{ m}^2\\)
c. \\(3\text{ m}^2\\)
d. \\(4\text{ m}^2\\)

Explanation:

Identify the given values

Using the Area of a Circle knowledge point

$$ \text{Total Area } (A_{\text{total}}) = 36\text{ m}^2 $$

$$ \text{Central Angle of Sector } (\theta) = 40^\circ $$

Calculate the sector area fraction

Using the Area of a Sector knowledge point

$$ \text{Fraction} = \frac{\theta}{360^\circ} = \frac{40^\circ}{360^\circ} = \frac{1}{9} $$

Compute the area of the sector

Using the Area of a Sector knowledge point

$$ A_{\text{sector}} = \frac{1}{9} \times A_{\text{total}} = \frac{1}{9} \times 36\text{ m}^2 = 4\text{ m}^2 $$

Answer:

• A. \(6\text{ m}^2\)
• B. \(2\text{ m}^2\)
• C. \(3\text{ m}^2\)
• D. \(4\text{ m}^2\) (Correct answer)