To find the area of a shaded sector of a circle, you can use the formula:
\[ \text{Area of the sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(\theta\) is the central angle of the sector in degrees,
- \(r\) is the radius of the circle.
In your case:
- \(\theta = 140^\circ\)
- \(r = 16 , \text{m}\)
Now plug the values into the formula:
\[ \text{Area of the sector} = \frac{140^\circ}{360^\circ} \times \pi (16 , \text{m})^2 \]
First, calculate \( (16 , \text{m})^2 \):
\[ (16 , \text{m})^2 = 256 , \text{m}^2 \]
Now substitute that value back into the equation:
\[ \text{Area of the sector} = \frac{140}{360} \times \pi \times 256 \]
Simplify \( \frac{140}{360} \):
\[ \frac{140}{360} = \frac{14}{36} = \frac{7}{18} \]
So:
\[ \text{Area of the sector} = \frac{7}{18} \times \pi \times 256 \]
Now calculate the area:
\[ \text{Area of the sector} = \frac{7 \times 256 \pi}{18} \]
Calculating \(7 \times 256\):
\[ 7 \times 256 = 1792 \]
Now divide by 18:
\[ \frac{1792}{18} \approx 99.5556 \]
Now multiply by \(\pi\):
\[ \text{Area of the sector} \approx 99.5556 \pi \]
Finally, you can approximate with \(\pi \approx 3.14159\):
\[ 99.5556 \pi \approx 99.5556 \times 3.14159 \approx 312.44 , \text{m}^2 \]
Therefore, the area of the shaded sector is approximately:
\[ \text{Area of the shaded sector} \approx 312.44 , \text{m}^2 \]
So, your response should be:
The area of the shaded sector is approximately 312.44 m².