Question

What is the area of the sector of a circle with θ
= 196 °
and a radius of 6 inches? Express your answer in terms of π




(1 point)
Responses

19.6π
in2
19.6piin2

5.4π
in2
5.4piin2

1176π
in2
1176piin2

32.7π
in2

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 in degrees,
- \(r\) is the radius of the circle.

Given:
- \(\theta = 196^\circ\)
- \(r = 6\) inches

Substituting the values into the formula:

\[
\text{Area} = \frac{196}{360} \times \pi \times (6^2)
\]
\[
= \frac{196}{360} \times \pi \times 36
\]
\[
= \frac{196 \times 36}{360} \times \pi
\]
\[
= \frac{7056}{360} \times \pi
\]
\[
= \frac{7056 \div 72}{360 \div 72} \times \pi
\]
\[
= \frac{98}{5} \times \pi
\]
\[
= 19.6 \pi
\]

Thus, the area of the sector is:

\[
\boxed{19.6\pi} \, \text{in}^2
\]