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

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

A=19.6π in.2
upper A equals 19.6 pi in. squared

A=4.2π in.2

Answer 1

To find the area of the sector of a circle given the central angle \( \theta \) and the radius \( r \), you can use the formula:

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

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

First, calculate \( r^2 \):

\[
r^2 = 7^2 = 49
\]

Now plug in the values into the area formula:

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

Simplify \( \frac{216}{360} \):

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

Now substitute that back into the area formula:

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

Calculate \( \frac{147}{5} \):

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

Thus the area of the sector is:

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

The correct answer is:

**A = 29.4π in²**