Question

question 5 of 10

what is the approximate area of the shaded sector in the circle shown below?

a. \\(20.36\text{ cm}^2\\)
b. \\(5.09\text{ cm}^2\\)
c. \\(5.65\text{ cm}^2\\)
d. \\(2.83\text{ cm}^2\\)

Explanation:

Identify the given values

Using the Diameter of a Circle knowledge point

$$ d = 3.6\text{ cm},\quad \theta = 180^\circ $$

Calculate the radius of the circle

Using the Radius of a Circle knowledge point

$$ r = \frac{d}{2} = \frac{3.6}{2} = 1.8\text{ cm} $$

Calculate the area of the shaded sector

Using the Area of a Sector knowledge point

$$ A = \frac{\theta}{360^\circ} \cdot \pi r^2 = \frac{180^\circ}{360^\circ} \cdot \pi (1.8)^2 = 0.5 \cdot 3.24\pi \approx 5.08938\text{ cm}^2 $$

Round to the nearest hundredth

Using the Area of a Sector knowledge point

$$ A \approx 5.09\text{ cm}^2 $$

Answer:

• A. \(20.36\text{ cm}^2\)
• B. \(5.09\text{ cm}^2\) (Correct answer)
• C. \(5.65\text{ cm}^2\)
• D. \(2.83\text{ cm}^2\)