Math worksheet for calculating the area of circle sectors and semi-circles.

Of course! Let's solve each problem step by step. The formula for the area of a sector of a circle is:

Area of Sector = (θ / 360°) × π × r²

Where:
- θ is the central angle in degrees
- r is the radius of the circle

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Problem 1: Find the area of the shaded sector

- Radius (r) = 2 cm
- Central angle (θ) = 60° (shaded part)

Simplified Version:
Area = (60 / 360) × π × (2)²
= (1/6) × π × 4
= (4/6)π = (2/3)π cm²

Rounded Answer:
(2/3) × π ≈ (2/3) × 3.14159 ≈ 2.09 cm²

✔ Answer = (2/3)π cm²
✔ Rounded Answer = 2.09 cm²

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Problem 2: Find the area of the unshaded sector

- Radius (r) = 7 m
- Shaded angle = 240° → So, unshaded angle = 360° - 240° = 120°

Simplified Version:
Area = (120 / 360) × π × (7)²
= (1/3) × π × 49
= (49/3)π m²

Rounded Answer:
(49/3) × π ≈ 16.333 × 3.14159 ≈ 51.31 m²

✔ Answer = (49/3)π m²
✔ Rounded Answer = 51.31 m²

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Problem 3: Find the area of the unshaded sector

- Radius (r) = 6 cm
- Shaded angle = 85° → So, unshaded angle = 360° - 85° = 275°

Simplified Version:
Area = (275 / 360) × π × (6)²
= (275 / 360) × π × 36
= (275 × 36 / 360) × π
= (275 × 1 / 10) × π *(since 36/360 = 1/10)*
= (275/10)π = (55/2)π cm²

Rounded Answer:
(55/2) × π = 27.5 × 3.14159 ≈ 86.39 cm²

✔ Answer = (55/2)π cm²
✔ Rounded Answer = 86.39 cm²

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Problem 4: Find the area of the shaded sector

- Radius (r) = 9 cm
- Central angle (θ) = 100° (shaded part)

Simplified Version:
Area = (100 / 360) × π × (9)²
= (5/18) × π × 81
= (5 × 81 / 18) × π
= (5 × 9 / 2) × π *(since 81 ÷ 9 = 9, 18 ÷ 9 = 2)*
= (45/2)π cm²

Rounded Answer:
(45/2) × π = 22.5 × 3.14159 ≈ 70.69 cm²

✔ Answer = (45/2)π cm²
✔ Rounded Answer = 70.69 cm²

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Problem 5: Find the area of a semi-circle that has a radius of 8 in.

A semi-circle is half of a full circle → so θ = 180°

Simplified Version:
Area = (180 / 360) × π × (8)²
= (1/2) × π × 64
= 32π in²

Rounded Answer:
32 × π ≈ 32 × 3.14159 ≈ 100.53 in²

✔ Answer = 32π in²
✔ Rounded Answer = 100.53 in²

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## ✔ Final Answers Summary:

1.
Answer = (2/3)π cm²
Rounded Answer = 2.09 cm²

2.
Answer = (49/3)π m²
Rounded Answer = 51.31 m²

3.
Answer = (55/2)π cm²
Rounded Answer = 86.39 cm²

4.
Answer = (45/2)π cm²
Rounded Answer = 70.69 cm²

5.
Answer = 32π in²
Rounded Answer = 100.53 in²

Let me know if you’d like to see diagrams or further explanations!