Let’s solve each problem step by step.
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Problem 1:
Circle with radius = 3 in, central angle = 40°
→ Arc length formula:
Arc Length = (θ/360) × 2πr
= (40/360) × 2 × π × 3
= (1/9) × 6π
= 6π/9 = 2π/3 ≈
2.09 inches
→ Sector Area formula:
Area = (θ/360) × πr²
= (40/360) × π × 9
= (1/9) × 9π =
π ≈ 3.14 square inches
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Problem 2:
Circle with radius = 6 yd, shaded sector angle = 260°
→ Arc length of arc EGF (the shaded part):
Arc Length = (260/360) × 2 × π × 6
= (13/18) × 12π
= (156π)/18 = 26π/3 ≈
27.23 yards
→ Sector Area:
Area = (260/360) × π × 6²
= (13/18) × 36π
= (468π)/18 = 26π ≈
81.68 square yards
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Problem 3:
Circle with diameter = 8 cm → radius = 4 cm, central angle = 135°
→ Arc length of arc AB:
Arc Length = (135/360) × 2 × π × 4
= (3/8) × 8π =
3π ≈ 9.42 cm
→ Sector Area:
Area = (135/360) × π × 4²
= (3/8) × 16π = 6π ≈
18.85 cm²
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Final Answer:
1. Length of arc KN = 2π/3 in (≈2.09 in), Area of Sector = π in² (≈3.14 in²)
2. Length of arc EGF = 26π/3 yd (≈27.23 yd), Area of Sector = 26π yd² (≈81.68 yd²)
3. Length of arc AB = 3π cm (≈9.42 cm), Area of Sector = 6π cm² (≈18.85 cm²)
Parent Tip: Review the logic above to help your child master the concept of geometry worksheet arc length sector area segment area answers.
