Question

Find the area of the shaded sector of the circle.
140 degrees140°16 m16 m



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Part 1
The area of the shaded sector is enter your response here msquared2.

Answer 1

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.**