To calculate the
area of a sector of a circle, we use the formula:
>
Area of Sector = (θ / 360°) × π × r²
Where:
-
θ is the central angle in degrees,
-
r is the radius of the circle,
-
π is approximately
3.1416 (unless otherwise specified — we’ll use 3.14 for simplicity unless asked for exact form).
---
Let’s solve each of the 6 sectors one by one.
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1. Angle = 35°, Radius = 10
Area = (35/360) × π × 10²
= (7/72) × π × 100
= (700/72) × π
= (175/18) × π
≈ (9.7222) × 3.14 ≈
30.53
✔ Answer: 30.53 (rounded to two decimal places)
---
2. Angle = 40°, Radius = 5
Area = (40/360) × π × 5²
= (1/9) × π × 25
= 25π/9
≈ 2.7778 × 3.14 ≈
8.73
✔ Answer: 8.73
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3. Angle = 55°, Radius = 8
Area = (55/360) × π × 8²
= (11/72) × π × 64
= (704/72) × π
= (88/9) × π
≈ 9.7778 × 3.14 ≈
30.71
✔ Answer: 30.71
---
4. Angle = 12°, Radius = 12
Area = (12/360) × π × 12²
= (1/30) × π × 144
= 144π/30
= 24π/5
≈ 4.8 × 3.14 ≈
15.07
✔ Answer: 15.07
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5. Angle = 70°, Radius = 6
Area = (70/360) × π × 6²
= (7/36) × π × 36
= 7 × π
≈ 7 × 3.14 =
21.98
✔ Answer: 21.98
*(Note: The 36 cancels out nicely here!)*
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6. Angle = 5°, Radius = 9
Area = (5/360) × π × 9²
= (1/72) × π × 81
= 81π/72
= 9π/8
≈ 1.125 × 3.14 ≈
3.53
✔ Answer: 3.53
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##
✔ Final Answers (rounded to two decimal places):
1.
30.53
2.
8.73
3.
30.71
4.
15.07
5.
21.98
6.
3.53
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📌 *Note: If your worksheet expects answers in terms of π (exact form), you can leave them as fractions times π (e.g., 7π for #5). But since it says “calculate,” and provides blank boxes, decimal approximations are appropriate.*
Let me know if you’d like to see the exact fractional forms too!
Parent Tip: Review the logic above to help your child master the concept of sector area worksheet.
