**Arc Length Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on length of arc of a sector.

The formula to find the length of arc is

**Problem 1 :**

Find the length of the arc that is bolded. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Problem 2 :**

Find the length of the arc that is bolded. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Problem 3 :**

Find the length of the arc highlighted in red color.(Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Problem 4 :**

In the diagram given below, if QRS is a central angle and m∠QRS = 81°, m∠SRT = 115°, and radius is 5 cm, then find the length of the arc QST. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Problem 5 :**

If m∠LMN = 19° and radius is 15 inches, then find the length of arc LN. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Problem 6 :**

In a circle, if the arc length of Arc AB is 18 cm and the measure of Arc AB is 39°, then find the radius of the circle. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)** **

**Problem 7 :**

In a circle, if the arc length of Arc AB is 19 inches and the radius is 29 inches, then find the measure of arc AB. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)** **

**Problem 8 :**

Find the length of the arc highlighted in red color. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Problem 1 :**

Find the length of the arc that is bolded. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Solution :**

**The formula to find the arc length is**

**= (Arc Measure / 360**°**) **⋅ 2**Π r**

**Plug r = 8, Arc Measure**** = 135**° and **Π **≈** 3.14**

≈ (135° / 360°) ⋅ 2 ⋅ 3.14 ⋅ 8

≈ 18.9

Hence, the length of the arc is about 18.9 yd.

Let us look at the next problem on "Arc length worksheet".

**Problem 2 :**

**Solution :**

**The formula to find the arc length is**

**= (Arc Measure / 360**°**) **⋅ 2**Π r**

**Plug r = 8, Arc Measure**** = 315**° and **Π **≈** 3.14**

≈ (315° / 360°) ⋅ 2 ⋅ 3.14 ⋅ 8

≈ 44

Hence, the length of the arc is about 44 cm.

Let us look at the next problem on "Arc length worksheet".

**Problem 3 :**

Find the length of the arc highlighted in red color. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Solution :**

**Given : **Diameter is 4 inches.

**Then, the radius is **

**= Diameter / 2**

**= 4 / 2 **

**= 2 inches**

**The formula to find the arc length is**

**= (Arc Measure / 360**°**) **⋅ 2**Π r**

**Plug r = 2, Arc Measure**** = 80**° and **Π **≈** 3.14**

≈ (80° / 360°) ⋅ 2 ⋅ 3.14 ⋅ 2

≈ 2.8

Hence, the length of the arc is about 2.8 inches.

Let us look at the next problem on "Arc length worksheet".

**Problem 4 :**

In the diagram given below, if QRS is a central angle and m∠QRS = 81°, m∠SRT = 115°, and radius is 5 cm, then find the length of the arc QST. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Solution :**

**To find the length of the arc QST, first we have to find the arc measure QST or the central angle **m∠QRT.

m∠QRT = m∠QRS + m∠SRT

m∠QRT = **81**° + 115°

m∠QRT = 196°

**The formula to find the arc length is**

**= (Central Angle / 360**°**) **⋅ 2**Π r**

**Plug r = 5, Central Angle**** = 196**° and **Π **≈** 3.14**

≈ (196° / 360°) ⋅ 2 ⋅ 3.14 ⋅ 5

≈ 17.1

Hence, the length of the arc is about 17.1 cm.

Let us look at the next problem on "Arc length worksheet".

**Problem 5 :**

If m∠LMN = 19° and radius is 15 inches, then find the length of arc LN. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Solution :**

**To find the length of the arc LN, first we have to find the arc measure LN**.

**By Inscribed Angle Theorem, we have**

**1/2 **⋅ Arc Measure = **m∠LMN**

**Multiply both sides by 2. **

**Arc Measure = ****2 **⋅ **m∠LMN**

**Arc Measure = ****2 **⋅ 1**9**°

**Arc Measure = 38****°**

**The formula to find the arc length is**

**= (Arc Measure / 360**°**) **⋅ 2**Π r**

**Plug r = 15, Arc Measure**** = 38**° and **Π **≈** 3.14**

≈ (38° / 360°) ⋅ 2 ⋅ 3.14 ⋅ 15

≈ 9.9

Hence, the length of the arc is about 9.9 inches.

Let us look at the next problem on "Arc length worksheet".

**Problem 6 :**

In a circle, if the arc length of Arc AB is 18 cm and the measure of Arc AB is 39°, then find the radius of the circle. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)** **

**Solution :**

**Given : **The arc length of Arc AB is 18 cm.

So, we have

**(Arc Measure / 360**°**) **⋅ 2**Π r = 18**

**Plug Arc Measure**** = 39**° and **Π **≈** 3.14**

(39° / 360°) ⋅ 2 ⋅ 3.14 ⋅ r ≈ 18

(39° / 360°) ⋅ 2 ⋅ 3.14 ⋅ r ≈ 18

0.1083 ⋅ 2 ⋅ 3.14 ⋅ r ≈ 18

0.68 ⋅ r ≈ 18

Divide both sides by 0.68.

r ≈ 18 / 0.68

r ≈ 26.5

Hence, the radius of the circle is about 26.5 cm.

Let us look at the next problem on "Arc length worksheet".

**Problem 7 :**

In a circle, if the arc length of Arc AB is 19 inches and the radius is 29 inches, then find the measure of arc AB. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)** **

**Solution :**

**Given : **The arc length of Arc AB is 19 inches.

So, we have

**(Arc Measure / 360**°**) **⋅ 2**Π r = 19**

**Plug r = 29 **and **Π **≈** 3.14**

(Arc Measure / 360°) ⋅ 2 ⋅ 3.14 ⋅ 29 ≈ 19

(Arc Measure / 360°) ⋅ 182.12 ≈ 19

(Arc Measure / 360°) ⋅ 182.12 ≈ 19

Multiply both sides by 360° / 182.12

Arc Measure ≈ 19 ⋅ 360° / 182.12

Arc Measure ≈ 19 ⋅ 360° / 182.12

Arc Measure ≈ 37.6°

Hence, the measure of arc AB is about 37.6°.

Let us look at the next problem on "Arc length worksheet".

**Problem 8 :**

Find the length of the arc highlighted in red color. (Take ∏ ≈ 3.14 and round your answer to one decimal place, if necessary)

**Solution :**

**From the given diagram, we have**

**m∠MCN + Measure of arc MON = 360**°

**Plug ****m∠MCN = 88**°

**88**° + **Measure of arc MON = 360**°

Subtract 88° from both sides.

**Measure of arc MON = 272**°

**Given : **Diameter is 4 inches.

**Then, the radius is**

**= Diameter / 2**

**= 10 / 2**

**= 5 ft**

**The formula to find the arc length is**

**= (Arc Measure / 360**°**) **⋅ 2**Π r**

**Plug r = 5, Arc Measure**** = 272**° and **Π **≈** 3.14**

≈ (272° / 360°) ⋅ 2 ⋅ 3.14 ⋅ 5

≈ 23.7 ft

Hence, the length of the arc is about 23.7 ft.

After having gone through the stuff given above, we hope that the students would have understood how to find arc length.

Apart from the stuff given above, if you want to know more about "Arc length of a sector", __please click here.__

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