💬 Arc Length & Sector Area: Mixed Practice & Reasoning (G-C.B.5)

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Derive and use arc length and sector area formulas. Read each problem. Draw or write to solve. Label your answer.

1. Arc: radius 6, central angle 90°. Length (exact)?

Work

Answer: ______________

2. Sector: radius 13, central angle 135°. Area (exact)?

Work

Answer: ______________

3. Arc: radius 13, central angle 150°. Length (exact)?

Work

Answer: ______________

4. Sector: radius 10, central angle 30°. Area (exact)?

Work

Answer: ______________

5. Arc: radius 2, central angle 120°. Length (exact)?

Work

Answer: ______________

6. Sector: radius 15, central angle 30°. Area (exact)?

Work

Answer: ______________

Answer key: 1) 3π · 2) 63 3/8 (507/8)π · 3) 10 5/6 (65/6)π · 4) 8 1/3 (25/3)π · 5) 1 1/3 (4/3)π · 6) 18 3/4 (75/4)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 — mixed practice with space to reason and check, 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: Show Your Thinking (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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