Question

What is the area of the sector of a circle with 0 = 216 degrees and a radius of 7 inches? Express your answer in terms of pi.

Answer 1

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

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

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

Given:
- \(\theta = 216\) degrees
- \(r = 7\) inches

We can substitute these values into the formula:

\[
\text{Area} = \frac{216}{360} \times \pi \times (7^2)
\]

First, we calculate \(7^2\):

\[
7^2 = 49
\]

Now we can substitute this back into the formula:

\[
\text{Area} = \frac{216}{360} \times \pi \times 49
\]

Next, simplify \(\frac{216}{360}\):

\[
\frac{216}{360} = \frac{216 \div 72}{360 \div 72} = \frac{3}{5}
\]

Now we substitute this into the area formula:

\[
\text{Area} = \frac{3}{5} \times \pi \times 49
\]

Now, multiply \(49\) by \(\frac{3}{5}\):

\[
\text{Area} = \frac{3 \times 49}{5} \pi = \frac{147}{5} \pi
\]

Thus, the area of the sector is:

\[
\boxed{\frac{147}{5} \pi} \text{ square inches}
\]