Question

Find the area of the shaded sector of the circle.
120 degrees120°28 m28 m

Answer 1

To find the area of the shaded sector of the circle, you can use the formula for the area of a sector:

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

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

In this case, you have:
- \(\theta = 120^\circ\)
- \(r = 28 \, \text{m}\)

Now, plug the values into the formula:

\[
\text{Area of sector} = \frac{120}{360} \times \pi \times (28)^2
\]

First, simplify \(\frac{120}{360}\):

\[
\frac{120}{360} = \frac{1}{3}
\]

Now calculate \((28)^2\):

\[
(28)^2 = 784
\]

Now, plug that into the equation:

\[
\text{Area of sector} = \frac{1}{3} \times \pi \times 784
\]

Next, calculate \(\frac{784}{3}\):

\[
\frac{784}{3} \approx 261.33
\]

Now, multiply by \(\pi\):

\[
\text{Area of sector} \approx 261.33 \times \pi \approx 820.56 \, \text{m}^2 \, (\text{using} \, \pi \approx 3.14)
\]

Thus, the area of the shaded sector is approximately:

\[
\text{Area of sector} \approx 820.56 \, \text{m}^2
\]

If you need the answer in terms of \(\pi\):

\[
\text{Area of sector} \approx \frac{784\pi}{3} \, \text{m}^2
\]

So, the area of the shaded sector is:

\[
261.33 \, \text{m}^2 \text{ (approximately)}, \text{ or } \frac{784\pi}{3} \, \text{m}^2 \text{ (exactly).}
\]