Question

Find the area of the shaded sector of the circle.
110 degrees110°28 m28 m



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Question content area bottom
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 following formula:

\[
\text{Area of Sector} = \frac{\theta}{360} \times \pi r^2
\]

where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.

For your question:
- \(\theta = 110^\circ\)
- \(r = 28 \, \text{m}\)

Now, substitute these values into the formula:

\[
\text{Area of Sector} = \frac{110}{360} \times \pi (28)^2
\]

Calculating \(28^2\):

\[
28^2 = 784
\]

Now substituting that into the area calculation:

\[
\text{Area of Sector} = \frac{110}{360} \times \pi \times 784
\]

Calculating \(\frac{110}{360}\):

\[
\frac{110}{360} = \frac{11}{36}
\]

Now substituting back into the equation:

\[
\text{Area of Sector} = \frac{11}{36} \times \pi \times 784
\]

Calculating \(\frac{11 \times 784}{36}\):

\[
11 \times 784 = 8624
\]

Now, divide this by \(36\):

\[
\frac{8624}{36} \approx 239.0
\]

Finally, multiply by \(\pi\) (approximately \(3.14159\)):

\[
\text{Area of Sector} \approx 239.0 \times 3.14159 \approx 751.39 \, \text{m}^2
\]

Thus, the area of the shaded sector is:

\[
\text{Area of the shaded sector} \approx 751.39 \, \text{m}^2
\]

You can round it to a suitable number of significant figures as per your requirement. The final answer is approximately:

\[
751.39 \, \text{m}^2
\]