Question

What is the area of the sector of a circle with
θ
=
216
°
and a radius of 7 inches? Express your answer in terms of pi(1 point)
Responses

19.6
π

i
n
2
19.6
π

i
n
2

4.2
π

i
n
2
4.2
π

i
n
2

49
π

i
n
2
49
π

i
n
2

29.4
π

i
n
2

Answer 1

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

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

where \( \theta \) is the angle in degrees, and \( r \) is the radius.

In this case, we have \( \theta = 216^\circ \) and \( r = 7 \) inches.

Plugging in the values:

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

First, calculate \( r^2 \):

\[
7^2 = 49
\]

Now, the formula becomes:

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

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

\[
\frac{216}{360} = \frac{3}{5} \quad (\text{Simplifying by dividing the numerator and denominator by 72})
\]

Now, substitute back into the area formula:

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

Calculating \( \frac{3 \times 49}{5} \):

\[
3 \times 49 = 147
\]

Thus:

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

Finally, to express \( \frac{147}{5} \) as a decimal:

\[
\frac{147}{5} = 29.4
\]

So, the area of the sector is:

\[
\text{Area} = 29.4 \pi \text{ in}^2
\]

The correct answer is:

**29.4**
**π**
**i**
**n**
**²**