Find the area of the shaded sector. Write your answer to the nearest hundredth: BD = 18 cm 136 Shaded Sector cm2 Blank 1:
The Correct Answer and Explanation is:
To determine the area of the shaded sector, apply the sector area formula:
Area=πr2×θ360\text{Area} = \pi r^2 \times \frac{\theta}{360}
Given:
- Radius (rr) = 18 cm
- Central angle (θ\theta) = 136°
First, calculate the area of the entire circle:
Circle Area=π×182=324π\text{Circle Area} = \pi \times 18^2 = 324\pi
Next, determine the fraction of the circle occupied by the sector:
136360=3490=1745\frac{136}{360} = \frac{34}{90} = \frac{17}{45}
Now, compute the sector area:
Sector Area=324π×1745\text{Sector Area} = 324\pi \times \frac{17}{45}
Using π≈3.14159\pi \approx 3.14159:
324×3.14159×1745324 \times 3.14159 \times \frac{17}{45}
324×3.14159×0.3778324 \times 3.14159 \times 0.3778
≈384.85 cm2\approx 384.85 \text{ cm}^2
Thus, the area of the shaded sector is approximately 384.85 cm².
A sector represents a portion of a circle, and its area depends on the central angle. The total area of the circle serves as the reference, with the sector occupying a fraction proportional to its angle. Larger angles yield greater sector areas, following direct proportionality. Calculations involve determining the fraction of the circle and multiplying it by the total area. Precision improves by carrying forward decimal approximations to avoid rounding errors. This approach ensures accurate results while maintaining mathematical rigor.
