Question content area top
Part 1
A denotes the area of the sector of a circle of radius r formed by the central angle thetaθ. Find the missing quantity.
requals=22 ​inches, thetaθequals=120 degrees120° ​,  Aequals=​?
Question content area bottom
Part 1
Aequals=enter your response here square inches
​(Type an integer or decimal rounded to three decimal places as​ needed.)

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

\[
A = \frac{1}{2} r^2 \theta
\]

Where:
- \( A \) is the area of the sector.
- \( r \) is the radius of the circle.
- \( \theta \) is the central angle in radians.

### Step 1: Convert the angle to radians.
We are given \( \theta = 120^\circ \). To convert degrees to radians, use the conversion:

\[
\theta \text{ (in radians)} = \theta \text{ (in degrees)} \times \frac{\pi}{180}
\]

\[
\theta = 120 \times \frac{\pi}{180} = \frac{2\pi}{3} \text{ radians}
\]

### Step 2: Apply the formula.
Now that we have \( \theta = \frac{2\pi}{3} \) and \( r = 22 \) inches, substitute these into the formula for the area of the sector:

\[
A = \frac{1}{2} \times 22^2 \times \frac{2\pi}{3}
\]

Now let's calculate the area.The area of the sector is approximately \( 506.844 \) square inches (rounded to three decimal places).

Would you like any further details or clarifications?

Here are 5 related questions for further practice:
1. What is the area of a sector when \( r = 10 \) inches and \( \theta = 90^\circ \)?
2. If the radius is doubled, how does the area of the sector change?
3. Convert \( 45^\circ \) to radians and find the area of the sector for \( r = 15 \) inches.
4. How do you find the length of the arc in a sector of a circle?
5. What would be the area of a full circle with radius \( r = 22 \) inches?

**Tip:** When dealing with angles in sector area problems, always ensure the angle is in radians before applying the formula.

A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. r = 22 inches, θ = 120°, A = ?

Learn how to find the area of a sector of a circle with radius 22 inches and a central angle of 120°. This problem covers key geometry concepts like circle sectors, radians conversion, and the sector area formula. Suitable for students in Grades 9-10.

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