Question

What is the area of the sector of a circle with θ=115°
and a radius of 6 cm? Include pi in your calculation.(1 point)
Responses

A=76.97 cm2
upper A equals 76.97 cm squared

A=6.02 cm2
upper A equals 6.02 cm squared

A=36.13 cm2
upper A equals 36.13 cm squared

A=113.10 cm2

Answer 1

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

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

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

Given:
- \( \theta = 115^\circ \)
- \( r = 6 \, \text{cm} \)

Now, substituting the values into the formula:

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

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now substituting this back into the formula:

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

Calculating \( \frac{115}{360} \times 36 \):

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

So, the area becomes:

\[
A = 11.5 \pi
\]

Now, we can approximate the value of \( A \) using \( \pi \approx 3.14 \):

\[
A \approx 11.5 \times 3.14 \approx 36.13 \, \text{cm}^2
\]

Thus, the area of the sector is:

\[
A = 36.13 \, \text{cm}^2
\]

Therefore, the correct response is:

**A=36.13 cm²**