Lesson Worksheet: Arc Lengths Mathematics • 10th Grade

In this worksheet, we will practice finding the arc length and the perimeter of a circular sector using radians and solve problems including real-life situations.


An arc has a measure of 2π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.

  • A9πœ‹
  • B3πœ‹
  • C2πœ‹
  • D18πœ‹
  • E6πœ‹


The diagram shows a sector of a circle of radius √15 cm and central angle √3 rad.

Find the length of the arc of the sector, giving your answer exactly.

  • A15√3 cm
  • B6√5 cm
  • C3√15 cm
  • D5√3 cm
  • E3√5 cm


Find the length of the arc of a circle of radius 3.1 cm that subtends an angle of 1.1 rad.


An arc on a circle with a radius of 12 has a length of 14. Determine the arc’s measure, giving your answer in radians as a fraction in its simplest form.

  • A105πœ‹
  • Bπœ‹105
  • C76
  • D210πœ‹
  • E67


An arc of a circle of radius 5 cm has a length of 3.5 cm. Find the angle subtended by the arc in radians.


An arc of a circle of radius π‘Ÿ cm subtends an angle of πœƒ rad. Given that the perimeter of this sector is 𝑃 cm, find an expression for πœƒ in terms of π‘Ÿ and 𝑃.

  • Aπ‘ƒβˆ’2π‘Ÿπ‘Ÿ
  • Bπ‘βˆ’2π‘Ÿ
  • Cπ‘ƒβˆ’2π‘Ÿ2π‘Ÿ
  • D𝑃+2π‘Ÿπ‘Ÿ
  • Eπ‘Ÿπ‘ƒβˆ’2π‘Ÿ


An arc of a circle has a length of 2.7 cm and it subtends an angle of 0.3 rad. Find the radius of the circle.


Find the perimeter of 𝐴𝐡𝐢𝐷 in the following diagram.


The shape of the base of a bottle consists of a line segment of length 5 cm that is connected to the arc of a circle of radius 3 cm as shown.

Find the length of the arc of the circle to one decimal place.


During a soccer game, a free kick is awarded at a point that is 25 yd away from the left goalpost, as shown in the diagram. The rules state that when a free kick takes place, the players of the opposing team must stand at least 10 yd away from the ball, that is, behind the circular arc 𝐴𝐡.

Point 𝐹 is where the ball lies, points 𝐢 and 𝐷 mark the edges of the goal, and points 𝐴 and 𝐡 mark the points on 𝐹𝐢 and 𝐹𝐷 that are 10 yd away from 𝐹.

Given that the goalmouth is 8 yd wide, calculate the perimeter of the shaded area 𝐴𝐡𝐢𝐷. Give your answer to the nearest yard.

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