LENGTH OF ARC WORKSHEET

Question 1 :

Find the length of the arc whose radius is 42 cm and central angle is 60° (Take π  ≈  3.14 and round your answer to the nearest hundredth, if necessary).

Question 2 :

Find the length of the arc whose radius is 10.5 cm and central angle is 36° (Take π  ≈  3.14 and round your answer to the nearest hundredth, if necessary).

Question 3 :

Find the length of the arc whose radius is 21 cm and central angle is 120° (Take π  ≈  3.14 and round your answer to the nearest hundredth, if necessary).

Question 4 :

Find the length of an arc, if the radius of circle is 14 cm and area of the sector is 63 square cm.

Question 5 :

Find the length of arc, if the perimeter of a sector is 45 cm and radius is 10 cm.

Question 6 :

Find the arc length whose central angle is 180° and perimeter of circle is 64 cm.

Question 7 :

Find the area of the sector whose arc length is 20 cm and radius is 7 cm.

Question 8 :

A pendulum swings through an angle of 30° and describes an arc length of 11 cm. Find the length of the pendulum.

Detailed Answer Key

Question 1 :

Find the length of the arc whose radius is 42 cm and central angle is 60° (Take π  ≈  3.14 and round your answer to the nearest hundredth, if necessary).

Answer :

Arc length is

=  (θ/360°) ⋅ 2πr

Substitute r  =  42, θ  =  60° and π  ≈  3.14. 

≈  (60°/360°) ⋅ 2 ⋅ (3.14) ⋅ 42

=  (1/6) ⋅ 263.76

=  43.96

So, the length of the arc is about 43.96 cm. 

Question 2 :

Find the length of the arc whose radius is 10.5 cm and central angle is 36° (Take π  ≈  3.14 and round your answer to the nearest hundredth, if necessary).

Answer :

Arc length is

=  (θ/360°) ⋅ 2πr

Substitute r  =  10.5 and θ  =  36° and π  ≈  3.14.

≈  (36°/360°) ⋅ 2 ⋅ (3.14) ⋅ 10.5

 =  (1/10) ⋅ 65.94

=  6.59

So, the length of the arc is about 6.59 cm. 

Question 3 :

Find the length of the arc whose radius is 21 cm and central angle is 120° (Take π  ≈  3.14 and round your answer to the nearest hundredth, if necessary).

Answer :

Arc length is

=  (θ/360°) ⋅ 2πr

Substitute r  =  21 and θ  =  120° and π  ≈  3.14. 

≈  (120°/360°) ⋅ 2 ⋅ (3.14) ⋅ 21

 =  (1/3) ⋅ 131.8

=  43.96

So, the length of the arc is about 43.96 cm.

Question 4 :

Find the length of an arc, if the radius of circle is 14 cm and area of the sector is 63 square cm.

Answer :

Area of the sector  =  63 square cm

lr/2  =  63

Substitute r  =  14 cm. 

l(14)/2  =  63

l(7)  =  63

l  =  9 cm

So, the required arc length is 9 cm.

Question 5 :

Find the length of arc, if the perimeter of a sector is 45 cm and radius is 10 cm.

Answer :

Perimeter of sector  =  45 cm

l + 2r  =  45

Substitute r  =  10 cm.

l + 2(10)  =  45

l + 20  =  45

l  =  45 - 20

l  =  25 cm

Question 6 :

Find the arc length whose central angle is 180° and circumference of the circle is 64 cm.

Answer :

Circumference of circle  =  64 cm

2πr  =  64

Arc length is

l  =  (θ/360°) ⋅ 2πr

Substitute θ  =  180° and 2πr  =  64.

  l  =  (180°/360°) ⋅ 64

l  =  (1/2) ⋅ 64

l  =  32 cm

l  =  32 cm

Question 7 :

Find the area of the sector whose arc length is 20 cm and radius is 7 cm.

Answer :

Area of sector  =  lr/2

Substitute l  =  20 and r  =  7.

Area of sector  =  (20 x 7) / 2

Area of sector  =  70 square units.

Question 8 :

A pendulum swings through an angle of 30° and describes an arc length of 11 cm. Find the length of the pendulum.

Answer :

Arc length of sector  =  11 cm

sector angle  =  30°

If the pendulum swings once, then it forms a sector and the radius of the sector is the length of the pendulum.

So,

l  =  (θ/360°) x 2πr

Substitute the known values and solve for r.

11  =  (30°/360°) x 2 x (22/7) x r

 11  =  (1/12) x 2 x (22/7) x r

r  =  (11 x 7 x 12)/(2 x 22)

r  =  7 x 3

r  =  21 cm

So, the length of pendulum is 21 cm.

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