# How to Find Arc Length and Sector Area? (+FREE Worksheet!)

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 sector of a circle, use this formula: 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 $$=\color{blue}{(\frac{θ}{180})πr}$$

### Arc Length and Sector Area – 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 $$=(\frac{θ}{180})πr$$ $$=(\frac{60}{180})π(24)=(\frac{1}{3})π(24)=8×3.14 \cong 25.1$$ $$cm$$

### Arc Length and Sector Area – Example 2:

Find the area of the sector. $$(π=3.14$$), $$r=6$$ $$ft$$, $$\theta=90^\circ$$

Solution:

Use this formula: Area of a sector $$=\color{blue}{πr^2 (\frac{θ}{360})}$$
Area of a sector $$=πr^2 (\frac{θ}{360})=(3.14)(6^2 )(\frac{90}{360})=(3.14)(36)(\frac{1}{4})=28.26$$$$ft^2$$

### Arc Length and Sector Area – 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 $$=(\frac{θ}{180})πr$$ $$=(\frac{45}{180})π(28)=(\frac{1}{4})π(28)=7×3.14 \cong 22$$ $$cm$$

### Arc Length and Sector Area – Example 4:

Find the area of the sector. $$(π=3.14), r=5$$ $$ft$$, $$\theta=80^\circ$$

Solution:

Use this formula: Area of a sector $$=\color{blue}{πr^2 (\frac{θ}{360})}$$
Area of a sector $$=πr^2 (\frac{θ}{360})=(3.14)(5^2 )(\frac{80}{360})=(3.14)(25)(\frac{2}{9}) =17.44$$$$ft^2$$

## Exercises for Finding Arc Length and Sector Area

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

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

• $$\color{blue}{22 \ cm}$$
• $$\color{blue}{24.9 \ ft}$$
• $$\color{blue}{23 \ ft}$$
• $$\color{blue}{17.8 \ m}$$

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