5 questions
10th - 10th Grade
Mathematics
Designed for Grade 10 mathematics, this free printable worksheet helps students calculate arc length from central angles measured in degrees and radians. The five multiple-choice questions require students to select rounded arc-length values for circle diagrams, a windshield-wiper sweep, and a fan-shaped arc, then work backward from a known arc length to find an angle in radians. Students apply the degree-based arc-length relationship, use the radian formula, and distinguish between finding an arc length and finding an angle. The varied problems connect symbolic geometry to practical contexts while reinforcing accurate substitution, degree-to-radian reasoning, and rounding to the requested place value. A complete answer key is included for efficient checking and feedback.
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WorksheetsAnswer Key25.87 units
5.24 units
7.07 units
115.2 cm
2.35 radians
This Grade 10 worksheet contains five multiple-choice problems on finding arc length from central angles in degrees or radians and finding a radian angle from a known arc length. Students apply the appropriate arc-length relationship, interpret circle measurements, and round answers as required in diagram-based and real-world problems.
Begin by modeling the degree-based arc-length formula, then contrast it with s = rθ when the angle is given in radians. Work through one circle problem with students before assigning the remaining diagram, windshield-wiper, and fan-arc questions; use the final fan problem to discuss how the formula can be rearranged to find an angle.
Watch for students substituting a degree measure directly into the radian formula, using the wrong relationship for the units provided, or confusing the radius with the arc length. In the fan problem, students may calculate another arc length instead of solving for the angle, while the windshield-wiper item may expose errors in converting the 120-degree sweep or rounding to the nearest tenth.
Wayground provides this worksheet as both a printable PDF and a digital quiz, with a complete answer key for all five multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital quiz.
In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the five multiple-choice arc-length items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while preserving its degree, radian, and arc-length practice.
Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, including downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
