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 Using 3.14 for pi

Answer 1

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

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

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

1. **Calculate the radius**:
The diameter of the circle is 18 inches, so the radius \( r \) is:

\[
r = \frac{18}{2} = 9 \text{ inches}
\]

2. **Plug in the values into the formula**:
Given \( \theta = 122^\circ \) and using \( \pi \approx 3.14 \):

\[
\text{Area of sector} = \frac{122}{360} \times 3.14 \times (9)^2
\]

3. **Calculate \( (9)^2 \)**:

\[
(9)^2 = 81
\]

4. **Continue with the area calculation**:

\[
\text{Area of sector} = \frac{122}{360} \times 3.14 \times 81
\]
Now calculate \( \frac{122}{360} \):

\[
\frac{122}{360} \approx 0.338888\ldots \text{ (can keep as a fraction for more accuracy)}
\]

5. **Now substitute and calculate the area**:

\[
\text{Area of sector} \approx 0.338888\ldots \times 3.14 \times 81
\]

First, calculate \( 3.14 \times 81 \):

\[
3.14 \times 81 = 254.34
\]

Then continue the multiplication:

\[
\text{Area of sector} \approx 0.338888 \times 254.34
\]

\[
\text{Area of sector} \approx 86.0519232
\]

Thus, rounding this to two decimal places, the area of the sector is:

\[
\text{Area of sector} \approx 86.05 \text{ square inches}
\]

So the final answer is:

\[
\boxed{86.05}
\]