Learn how to find the arc length and sector area of a circle using the following step-by-step guide with examples.

## Step by step guide to find arc length and sector area of circles

- To find a
**Area of a sector**\(=\color{blue}{πr^2 (\frac{θ}{360})}\)

\(r\) is the radius of the circle and θ is the central angle of the sector. - To find the arc of a sector of a circle
**,**use this formula:**Arc of a sector**\(=\color{blue}{(\frac{θ}{180})πr}\)

### Example 1:

Find the length of the arc. Round your answers to the nearest tenth. \((π=3.14) r=24\) cm, \(\theta=60^\circ\)

**Solution:**

Use this formula: **length of a sector** \(=\color{blue}{(\frac{θ}{180})πr}\)

length of a sector \(=(\frac{60}{180})π(24)=(\frac{1}{3})π(24)=8×3.14 \cong 25.12 \) cm

### Example 2:

Find the area of the sector. \(r=6\) ft, \(\theta=90^\circ\)

**Solution**:

Use this formula: **Area of a sector** \(=\color{blue}{πr^2 (\frac{θ}{360})}\)

Area of a sector \(=πr^2 (\frac{θ}{360})=(3.14)(6^2 )(\frac{90}{360})=(3.14)(36)(\frac{1}{4})≅28.26 \)

### Example 3:

Find the length of the arc. Round your answers to the nearest tenth. \((π=3.14) r=28\) cm, \(\theta=45^\circ\)

**Solution**:

Use this formula: length of a sector \(=\color{blue}{(\frac{θ}{180})πr}\)

length of a sector \(=(\frac{45}{180})π(28)=(\frac{1}{4})π(28)=7×3.14 \cong 22\) cm

### Example 4:

Find the area of the sector. \(r=5 \) ft, \(\theta=80^\circ\)

**Solution**:

Use this formula: Area of a sector \(=\color{blue}{πr^2 (\frac{θ}{360})}\)

Area of a sector \(=πr^2 (\frac{θ}{360})=(3.14)(5^2 )(\frac{80}{360})≅17.4 \)

## Exercises

### Find the length of each arc. Round your answers to the nearest tenth.

- \(\color{blue}{r = 28 \ cm, \theta = 45^\circ}\)
- \(\color{blue}{r = 15 \ ft, \theta = 95^\circ}\)
- \(\color{blue}{r = 22 \ ft, \theta = 60^\circ}\)
- \(\color{blue}{r = 12 \ m, \theta = 85^\circ}\)

### Download Arc Length and Sector Area Worksheet

- \(\color{blue}{22 \ cm}\)
- \(\color{blue}{25 \ ft}\)
- \(\color{blue}{23 \ ft}\)
- \(\color{blue}{18 \ m}\)