ARC MEASURE AND ARC LENGTH WORKSHEET

Question 1 :

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

Question 2 :

The arc length of a sector is 66 cm and the central angle is 30°. Find its radius.

Question 3 :

The length of arc of a sector is 22 cm and its radius is 10.5 cm. Find its central angle.

Question 4 :

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°.

Answer :

Arc length is

=  (θ/360°) ⋅ 2πr

Substitute r  =  42, θ  =  60° and π  ≈  22/7. 

≈  (60°/360°) x 2 x (22/7) x 42

=  (1/6) x 264

=  44

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

Question 2 :

The arc length of a sector is 66 cm and the central angle is 30°. Find its radius.

Answer :

Arc length of sector  =  66 cm

Sector angle θ  =  30°

Formula for length of arc is

l  =  (θ/360) x 2πr

Substitute the known values and solve for r.

66  =  (30°/360°) x 2 x (22/7) x r

 66  =  (1/12) x 2 x 22 x r

r  =  (66 x 12)/(2 x 22)

r  =  126 cm

Question 3 :

The length of arc of a sector is 22 cm and its radius is 10.5 cm. Find its central angle.

Answer :

Arc length of sector  =  22 cm

radius  =  10.5 cm 

Formula for length of the arc is

l  =  (θ/360°) x 2πr

Substitute the known values and solve for θ.

22  =  (θ/360) x 2 x (22/7) x 10.5

 22  =  (θ/360) x 2 x 22 x 1.5

θ  =  (22 x 360)/(2 x 22 x 1.5)

=  180/1.5

θ  =  120°

Question 4 :

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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