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Lesson: Arc Length

Sample Question Videos

Worksheet • 25 Questions • 4 Videos

Q1:

Circle 𝑀 has a radius of 12 cm where the length of 𝐢 𝐡 is 16 cm. Find the length of arc 𝐢 𝐡 giving the answer to two decimal places.

Q2:

Find the length of the blue arc given the radius of the circle is 8 cm. Give the answer to one decimal place.

Q3:

If π‘š ∠ 𝐴 = 7 6 ∘ and the radius of the circle equals 3 cm, find the length of the major arc 𝐡 𝐢 .

Q4:

An arc has a measure of 2 πœ‹ 3 radians and a radius of 9. Work out the length of the arc, giving your answer in terms of πœ‹ , in its simplest form.

  • A 6 πœ‹
  • B 2 πœ‹
  • C 1 8 πœ‹
  • D 9 πœ‹
  • E 3 πœ‹

Q5:

A circle has a radius of 7.22 cm. Find the central angle that subtends an arc of length 12.53 cm, giving the answer to the nearest second.

  • A 9 9 2 6 β€² 4 β€² β€² ∘
  • B 6 6 1 7 β€² 2 2 β€² β€² ∘
  • C 3 3 0 β€² 5 3 β€² β€² ∘
  • D 1 4 9 9 β€² 6 β€² β€² ∘
  • E 6 6 1 β€² 4 7 β€² β€² ∘

Q6:

A circle has a radius of 7.19 cm. Find the central angle that subtends an arc of length 11.21 cm, giving the answer to the nearest second.

  • A 8 9 1 9 β€² 4 9 β€² β€² ∘
  • B 5 9 3 3 β€² 1 3 β€² β€² ∘
  • C 3 6 4 4 β€² 5 7 β€² β€² ∘
  • D 1 3 3 5 9 β€² 4 4 β€² β€² ∘
  • E 7 3 2 9 β€² 5 3 β€² β€² ∘

Q7:

An arc covers 2 9 of a circle’s circumference and the circle has a radius of 78 cm. Find, to the nearest hundredth, the measure and the length of the arc, using 2 2 7 as an approximation for πœ‹ .

  • A 8 0 ∘ , 108.91 cm
  • B 4 0 ∘ , 108.91 cm
  • C 4 0 ∘ , 54.45 cm
  • D 8 0 ∘ , 54.45 cm

Q8:

The radius of a sundial is 35 cm and the shadow changes at a rate of 1 5 ∘ every hour. Find in terms of πœ‹ the arc length of the rotation of the shadow after 10 hours.

  • A 1 7 5 6 πœ‹ cm
  • B 1 7 5 1 2 πœ‹ cm
  • C 1 0 5 2 πœ‹ cm
  • D 1 7 5 3 πœ‹ cm

Q9:

The radius of a sundial is 26 cm and the shadow changes at a rate of 1 5 ∘ every hour. Find in terms of πœ‹ the arc length of the rotation of the shadow after 4 hours.

  • A 2 6 3 πœ‹ cm
  • B 1 3 3 πœ‹ cm
  • C 7 8 5 πœ‹ cm
  • D 5 2 3 πœ‹ cm

Q10:

The length of an arc in a circle is 1 . 2 π‘Ÿ where π‘Ÿ is the radius of the circle. Find the central angle subtending the arc in radians giving the answer to one decimal place.

Q11:

The length of an arc in a circle is 2 π‘Ÿ where π‘Ÿ is the radius of the circle. Find the central angle subtending the arc in degrees giving the answer to the nearest second.

  • A 1 1 4 3 5 β€² 3 0 β€² β€² ∘
  • B 2 4 6 2 2 β€² 1 9 β€² β€² ∘
  • C 2 3 4 5 4 β€² 4 6 β€² β€² ∘
  • D 1 2 6 3 β€² 3 β€² β€² ∘

Q12:

A circle has a central angle of 6 4 5 4 β€² 5 8 β€² β€² ∘ which subtends an arc of length 4 πœ‹ cm. Find the diameter of the circle to the nearest centimetre.

Q13:

In the given figure, which of the following would represent the minor arc passing through 𝐡 and 𝐢 ?

  • A 𝐡 𝐢
  • B οƒͺ 𝐢 𝐡
  • C 𝐡 𝐢
  • D οƒͺ 𝐡 𝐢
  • E βƒ–     βƒ— 𝐡 𝐢

Q14:

Calculate the length of an arc on Earth’s surface that subtends an angle of 7 minutes at Earth’s centre knowing that 1 = 1 6 0 m i n u t e d e g r e e s of a degree. Take Earth’s radius to be 3 960 miles.

  • A 8.063 miles
  • B 57.6 miles
  • C 345.58 miles
  • D 2.89 miles
  • E 172.79 miles

Q15:

An arc in a circle measures 1 6 πœ‹ π‘Ÿ . What angle does it subtend?

Q16:

In the given figure, the circumference is 15 and π‘š ∠ 𝐴 𝑂 𝐡 is 6 0 ∘ . Find the length of 𝐴 𝐡 .

  • A 5 2
  • B 2 πœ‹ 4 5 2
  • C 5
  • D √ 1 5 πœ‹ 3
  • E 5 4

Q17:

Given that βƒ–     βƒ— 𝐴 𝐢 is a tangent to the circle 𝑀 , where it touches it at the point 𝐴 , 𝐡 𝑀 = 3 6 c m , and 𝐴 𝐢 = 5 4 c m , find the length of 𝐴 𝐷 .

Q18:

𝑀 is a circle of radius 19 cm. Determine, to the nearest hundredth, the length of 𝐡 𝐷 .

Q19:

The radius of a circle is 15 cm and the arc length of a sector is 16 cm. Find the central angle giving the answer to the nearest second.

  • A 6 1 6 β€² 5 6 β€² β€² ∘
  • B 5 3 7 β€² 3 0 β€² β€² ∘
  • C 5 7 1 7 β€² 4 5 β€² β€² ∘
  • D 7 3 8 β€² 2 2 β€² β€² ∘

Q20:

For the given figure, 𝑂 is the center of the circle and πœƒ is the measure of arc 𝑙 .

Write down an expression for the circumference of the circle.

  • A 2 πœ‹ π‘Ÿ
  • B 2 π‘Ÿ
  • C πœ‹ π‘Ÿ 2
  • D πœ‹ π‘Ÿ
  • E 2 πœ‹ π‘Ÿ 2

If πœƒ is measured in degrees, what fraction of the circle’s circumference is arc 𝑙 ?

  • A πœƒ 3 6 0
  • B πœƒ π‘Ÿ
  • C 3 6 0 πœƒ
  • D πœƒ 1 8 0
  • E 1 8 0 πœƒ

Write an expression for the length of arc 𝑙 , given that πœƒ is measured in degrees.

  • A πœƒ 3 6 0 Γ— 2 πœ‹ π‘Ÿ
  • B πœƒ 3 6 0 Γ— 2 π‘Ÿ
  • C πœƒ 1 8 0 Γ— 2 πœ‹ π‘Ÿ
  • D πœƒ 3 6 0 Γ— π‘Ÿ
  • E πœƒ 3 6 0 Γ— πœ‹ π‘Ÿ

Q21:

Given that 𝐴 𝑀 = 1 1 c m , find the length of 𝐴 𝐡 𝐢 rounded to the nearest integer.

Q22:

The area of a circular sector is 815.1 cm2 and the central angle is 6 2 ∘ . Find the arc length of the sector giving the answer to the nearest centimetre.

Q23:

Determine, to the nearest hundredth, the length of 𝑍 π‘Œ .

Q24:

What angle is subtended by an arc of length 20 in a circle of circumference 80?

Q25:

l e n g t h o f t h e a r c c i r c u m f e r e n c e o f t h e c i r c l e m e a s u r e o f t h e a r c = β‹― .

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