🧠 Arc Length & Sector Area: Show Your Thinking (G-C.B.5)

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Derive and use arc length and sector area formulas. Solve each problem and show your work.

1. Arc: radius 9, central angle 45°. Length (exact)?

Show your work

2. Sector: radius 7, central angle 72°. Area (exact)?

Show your work

3. Arc: radius 12, central angle 90°. Length (exact)?

Show your work

4. Sector: radius 14, central angle 120°. Area (exact)?

Show your work

5. Sector: radius 2, central angle 120°. Area (exact)?

Show your work

6. Arc: radius 6, central angle 135°. Length (exact)?

Show your work

Explain: How did you solve problem 1? Could you check it another way?

Answer key: 1) 2 1/4 (9/4)π · 2) 9 4/5 (49/5)π · 3) 6π · 4) 65 1/3 (196/3)π · 5) 1 1/3 (4/3)π · 6) 4 1/2 (9/2)π

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Worksheets › Grade 10 Math (Geometry) › Arc Length & Sector Area › Arc Length & Sector Area

Grade 10 (ages 15–16)Numbers & mathsFree printable PDF

About this grade 10 worksheet

Free Grade 10 Geometry math worksheet (Common Core G-C.B.5): arc length & sector area — problems with space to show work and explain reasoning, with answer key. Skill: Derive and use arc length and sector area formulas. Level: Grade 10 — also suits Year 11 (UK).

For teachers: skills & standards

CCSS G-C.B.5: Derive and use arc length and sector area formulas
Works as a morning-work page, a centre/station activity, homework or an early-finisher task.

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What age is it for?

It is designed for Grade 10 (ages 15–16), but use it with any child who is ready.

What skills does it build?

Derive and use arc length and sector area formulas.

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More “Arc Length & Sector Area” printables (g-c.b.5: derive and use arc length and sector area formulas)

Arc Length & Sector Area: Practice A (G-C.B.5) · Arc Length & Sector Area: Practice B (G-C.B.5) · Arc Length & Sector Area: Mixed Practice & Reasoning (G-C.B.5) · Arc Length & Sector Area: Quick Check (G-C.B.5)

All 5 arc length & sector area sheets → · Grade 10 Math (Geometry): all 10 skills → · All Common Core grades

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