Question

Question
What is the area of the sector of a circle with θ=122°
and a diameter of 18 inches? Write your answer to two decimal places.(1 point)
A=
π in.2

Answer 1

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

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

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

Given:
- Diameter = 18 inches, therefore the radius \( r = \frac{18}{2} = 9 \) inches,
- \( \theta = 122^\circ \).

Now, plug in the values into the formula:

\[
A = \frac{122}{360} \times \pi \times (9)^2
\]
\[
A = \frac{122}{360} \times \pi \times 81
\]
\[
A = \frac{122 \times 81}{360} \times \pi
\]
\[
A = \frac{9872}{360} \times \pi
\]
\[
A = 27.4667 \times \pi \, \text{in}^2
\]

Now calculate the numerical value:

\[
A \approx 27.4667 \times 3.14159 \approx 86.252 in^2
\]

Rounding to two decimal places, the area of the sector is:

\[
A \approx 86.25 \, \text{in}^2
\]

So the final answer is approximately:

\[
A \approx 86.25 \, \text{in}^2
\]