Lesson Worksheet: Arc Lengths and Sectors: Degrees Mathematics

In this worksheet, we will practice finding the arc length and the area of a sector given the angle measure in degrees.

Q1:

Given that 𝐴𝑀=11cm, find the length of 𝐴𝐡𝐢 rounded to the nearest integer.

Q2:

What is the length of the arc subtended by a central angle of 261∘ on a circle of radius π‘Ÿ?

  • A2980πœ‹π‘Ÿ
  • B2920πœ‹π‘Ÿ
  • C2940πœ‹π‘Ÿ
  • D2910πœ‹π‘Ÿ

Q3:

An arc on a circle with a radius of 50 has a length of 115. Determine the arc’s measure to the nearest tenth of a degree.

Q4:

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

Q5:

An arc covers 29 of a circle’s circumference and the circle has a radius of 78 cm. Find the measure and the length of the arc using 227 as an approximation for πœ‹, rounding the length to the nearest hundredth..

  • A40∘, 54.45 cm
  • B80∘, 108.91 cm
  • C40∘, 108.91 cm
  • D80∘, 54.45 cm

Q6:

The area of a circular sector is 815.1 cm2 and the central angle is 62∘. Find the arc length of the sector giving the answer to the nearest centimeter.

Q7:

lengthofthearccircumferenceofthecirclemeasureofthearc=β‹―.

Q8:

The figure shows square 𝐴𝐡𝐢𝐷 inscribed in a circle with center 𝑀. Given that the radius of the circle with center 𝑀 is 32 cm, find the perimeter of the shaded region. Give your answer to the nearest centimeter.

Q9:

In the given figure, the circumference is 15 and π‘šβˆ π΄π‘‚π΅ is 60∘. Find the length of 𝐴𝐡.

  • A√15πœ‹3
  • B2πœ‹45
  • C54
  • D5
  • E52

Q10:

Given that 𝑀𝐴=41, determine, to the nearest whole number, the length of arc 𝐴𝐢 and the area of the shaded region.

  • A64 cm, 480 cm2
  • B32 cm, 1,320 cm2
  • C129 cm, 4,441 cm2
  • D32 cm, 1,800 cm2

This lesson includes 49 additional questions and 322 additional question variations for subscribers.

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