Question

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

Answer 1

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

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

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

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

Let's substitute the values into the formula:

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

Calculating \( (7)^2 \):

\[
(7)^2 = 49
\]

Now substituting that into the equation:

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

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

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

So we can rewrite the area \( A \):

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

Now multiply:

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

Thus, the area of the sector is:

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