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

A=49π in.2
upper A equals 49 pi in. squared

A=29.4π in.2
upper A equals 29.4 pi in. squared

A=4.2π in.2
upper A equals 4.2 pi in. squared

A=19.6π in.2

Answer 1

To find the area of a sector of a circle, you 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,
- \( r \) is the radius.

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

Now, substitute the values into the formula:

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

First, calculate \( 7^2 \):

\[
7^2 = 49
\]

Now substitute that back into the formula:

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

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

\[
\frac{216}{360} = \frac{3}{5} \text{ (when simplified)}
\]

Now substitute this value back in:

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

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

\[
A = \frac{147}{5} \pi
\]

To convert \( \frac{147}{5} \) into a mixed number or decimal:

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

So, the area of the sector is:

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

Thus, the correct answer is:

**A=29.4π in.²**