Let’s solve each example step by step using the formulas given in the table.
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1. Circumference Example (radius = 3 in.)
Formula:
Circumference = 2πr or πd
We’re given radius r = 3 inches.
So, use 2πr:
→ 2 × π × 3 = 6π inches
If we want a decimal answer, use π ≈ 3.14:
→ 6 × 3.14 = 18.84 inches
✔ Final Answer for this example:
6π in. or about 18.84 in.
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2. Arc Length Example (radius = 7 m, angle = 100°)
Formula:
Arc Length = (2πrθ) / 360
Plug in r = 7, θ = 100:
→ (2 × π × 7 × 100) / 360
= (1400π) / 360
Simplify fraction: divide numerator and denominator by 40 → 35π / 9
Decimal? Use π ≈ 3.14:
→ 35 × 3.14 = 109.9
→ 109.9 ÷ 9 ≈ 12.21 meters
✔ Final Answer for this example:
35π/9 m or about 12.21 m
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3. Area of a Circle Example (radius = 9 cm)
Formula:
Area = πr²
r = 9 → r² = 81
→ π × 81 = 81π cm²
Decimal: 81 × 3.14 = 254.34 cm²
✔ Final Answer for this example:
81π cm² or about 254.34 cm²
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4. Sector Area Example (radius = 5 ft, angle = 70°)
Formula:
Sector Area = (πr²θ) / 360
r = 5 → r² = 25
θ = 70
→ (π × 25 × 70) / 360
= (1750π) / 360
Simplify: divide numerator and denominator by 10 → 175π / 36
Decimal: 175 × 3.14 = 549.5
→ 549.5 ÷ 36 ≈ 15.26 ft²
✔ Final Answer for this example:
175π/36 ft² or about 15.26 ft²
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Final Answer:
- Circumference example:
6π in. or ~18.84 in.
- Arc Length example:
35π/9 m or ~12.21 m
- Area of Circle example:
81π cm² or ~254.34 cm²
- Sector Area example:
175π/36 ft² or ~15.26 ft²
Parent Tip: Review the logic above to help your child master the concept of finding arc length worksheet.
