Question

what is the area of a sector of a circle with 0=115 degrees and a radius of 6 cm? include pi in your calculation.

Answer 1

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

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

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

In this case, \(\theta = 115\) degrees and \(r = 6\) cm. Plugging in these values:

\[
\text{Area} = \frac{115}{360} \times \pi \times (6)^2
\]

Calculating \(6^2\):

\[
6^2 = 36
\]

Now substitute it back into the equation:

\[
\text{Area} = \frac{115}{360} \times \pi \times 36
\]

Next, calculate \(\frac{115 \times 36}{360}\):

\[
\frac{115 \times 36}{360} = \frac{4140}{360}
\]

Now simplify \(\frac{4140}{360}\):

\[
\frac{4140 \div 180}{360 \div 180} = \frac{23}{2}
\]

Thus, the area of the sector is:

\[
\text{Area} = \frac{23}{2} \pi \quad \text{cm}^2
\]

So the final answer is:

\[
\text{Area} = \frac{23}{2} \pi \, \text{cm}^2
\]

Answer 2

options are

36.13 cm^2

6.02 cm^2

113.10 cm^2

76.97 cm^2

Answer 3

Let's calculate the area of the sector once again, including the numerical value to match to the options provided.

The formula for the area of a sector is:

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

Given:
- \(\theta = 115\) degrees
- \(r = 6\) cm

Substituting the values:

\[
\text{Area} = \frac{115}{360} \times \pi \times (6)^2
\]

First, calculate \(6^2 = 36\):

\[
\text{Area} = \frac{115}{360} \times \pi \times 36
\]

Now calculate \(\frac{115 \times 36}{360}\):

\[
\frac{115 \times 36}{360} = \frac{4140}{360} = 11.5
\]

Now, substituting back into the area formula:

\[
\text{Area} = 11.5 \times \pi \approx 11.5 \times 3.14 \approx 36.13 \, \text{cm}^2
\]

So the area of the sector is approximately:

\[
\text{Area} \approx 36.13 \, \text{cm}^2
\]

Thus, the correct answer from the options provided is:

\[
\text{Option: } 36.13 \, \text{cm}^2
\]