**Length of arc worksheets :**

Here we are going to see some practice problems on length of arc.

**Length of arc = (θ/360) x 2Πr**

here θ - central angle

r - radius

Now we are going to see example problems based on this formula.

(1) Find the length of arc whose radius is 42 cm and central angle is 60°

(2) Find the length of arc whose radius is 21 cm and central angle is 120°

(3) Find the length of arc whose radius is 35 cm and central angle is 72°

(4) Find the length of arc whose radius is 10.5 cm and central angle is 36°

(5) Find the length of arc whose radius is 14 cm and central angle is 5°

(6) Find the length of arc whose radius is 28 cm and central angle is 90°

(7) Find the length of arc whose radius is 14 cm and central angle is 288°

(8) Find the length of arc whose radius is 10.5 cm and central angle is 45°

(9) Find the length of arc whose radius is 35 cm and central angle is 18°

(10) Find the length of arc whose radius is 21 cm and central angle is 30°

**Question 1 :**

Find the length of arc whose radius is 42 cm and central angle is 60°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 60° and radius (r) = 42 cm

= (60°/360) x 2 x (22/7) x 42

= (1/6) x 2 x 22 x 6

= 2 x 22

= 44 cm

Hence, the length of arc is 44 cm.

**Question 2 :**

Find the length of arc whose radius is 21 cm and central angle is 120°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 120° and radius (r) = 21 cm

= (120°/360) x 2 x (22/7) x 21

= (1/3) x 2 x 22 x 3

= 2 x 22

= 44 cm

Hence, the length of arc = 44 cm

**Question 3 :**

Find the length of arc whose radius is 35 cm and central angle is 72°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 72° and radius (r) = 35 cm

= (72°/360) x 2 x (22/7) x 35

= (2/10) x 2 x 22 x 5

= (1/5) x 2 x 22 x 5

= 44 cm

Hence, length of arc = 44 cm

**Question 4 :**

Find the length of arc whose radius is 10.5 cm and central angle is 36°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 36° and radius (r) = 10.5 cm

= (36°/360) x 2 x (22/7) x 10.5

= (1/10) x 2 x (22/7) x 10.5

= (1/5) x (22/7) x 10.5

= (22/7) x 2.1

= 22 x 0.3

= 6.6 cm

Hence, the length of arc = 6.6 cm

**Question 5 :**

Find the length of arc whose radius is 14 cm and central angle is 5°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 5° and radius (r) = 14 cm

= (5°/360) x 2 x (22/7) x 14

= (1/72) x 2 x 22 x 2

= (1/36) x 2 x 22

= (1/18) x 22

= (1/9) x 11

= 11/9

= 1.22 cm

Hence, the length of arc = 1.22 cm

**Question 6 :**

Find the length of arc whose radius is 28 cm and central angle is 90°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 90° and radius (r) = 28 cm

= (90°/360) x 2 x (22/7) x 28

= (1/4) x 2 x 22 x 4

= 2 x 22

= 44 cm

Hence, the length of arc = 44 cm

**Question 7 :**

Find the length of arc whose radius is 14 cm and central angle is 288°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 288° and radius (r) = 14 cm

= (288°/360) x 2 x (22/7) x 14

= (144/180) x 2 x 22 x 2

= (72/90) x 2 x 22

= (72/45) x 2 x 22

= (72 x 22 x 2)/45

= 3168/45

= 70.4 cm

Hence, the length of arc = 70.4 cm

**Question 8 :**

Find the length of arc whose radius is 10.5 cm and central angle is 45°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 45° and radius (r) = 10.5 cm

= (45°/360) x 2 x (22/7) x 10.5

= (9/72) x 2 x 22 x 1.5

= (1/8) x 2 x 22 x 1.5

= (1/4) x 22 x 1.5

= (1/2) x 11 x 1.5

= 8.25 cm

Hence, the length of arc = 8.25 cm

Let us see the solution of next problem on "Length of arc worksheets"

**Question 9 :**

Find the length of arc whose radius is 35 cm and central angle is 18°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 18° and radius (r) = 35 cm

= (18°/360) x 2 x (22/7) x 35

= (1/20) x 2 x 22 x 5

= (1/10) x 2 x 22 x 5

= (1/2) x 2 x 22

= 11 cm

Hence, the length of arc = 11 cm

Let us see the solution of next problem on "Length of arc worksheets"

**Question 10 :**

Find the length of arc whose radius is 21 cm and central angle is 30°

**Solution :**

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 35° and radius (r) = 35 cm

= (30°/360) x 2 x (22/7) x 35

= (1/12) x 2 x 22 x 5

= (1/6) x 22 x 5

= (1/3) x 11 x 5

= 55/3 cm

= 18.3 cm

Hence, the length of arc = 18.3 cm

After having gone through the problems explained above, we hope that the students would have understood the stuff given on "Length of arc worksheets".

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