Area of Circles and Sectors Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We’ll use π = 3.14 as instructed.

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Problem 1: Circle with diameter 18 yd

Area of a circle = π × r²
Diameter = 18 yd → Radius = 18 ÷ 2 = 9 yd
Area = 3.14 × 9² = 3.14 × 81 = 254.34 yd²

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Problem 2: Circle with radius 28 ft

Area = π × r² = 3.14 × 28²
28² = 784
Area = 3.14 × 784 = 2461.76 ft²

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Problem 3: Circle with radius 5.6 m

Area = 3.14 × (5.6)²
5.6² = 31.36
Area = 3.14 × 31.36 = 98.4704 m² → Round to two decimals? Let’s keep it as is for now, but usually we round to hundredths: 98.47 m²

Wait — let me recalculate:
3.14 × 31.36
= 3 × 31.36 = 94.08
+ 0.14 × 31.36 = 4.3904
Total = 94.08 + 4.3904 = 98.4704 → So 98.47 m² if rounded to two decimal places.

But since the input had one decimal (5.6), maybe keep two decimals in answer. Okay, 98.47 m²

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Now sectors:

Formula for sector area = (θ/360) × π × r²

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Problem 4: Sector with angle 40°, radius 3.5 yd

First, full circle area = 3.14 × (3.5)² = 3.14 × 12.25 = 38.465
Sector fraction = 40/360 = 1/9
Area = 38.465 ÷ 9 ≈ 4.2739 → Round to two decimals: 4.27 yd²

Check:
(40/360) × 3.14 × 12.25
= (1/9) × 38.465 = 4.27388... → 4.27 yd²

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Problem 5: Sector with angle 70°, radius 7.5 ft

Full circle area = 3.14 × (7.5)² = 3.14 × 56.25 = 176.625
Sector fraction = 70/360 = 7/36
Area = (7/36) × 176.625
First, 176.625 ÷ 36 = 4.90625
Then ×7 = 34.34375 → 34.34 ft² (rounded)

Or directly:
(70/360) × 3.14 × 56.25
= (7/36) × 176.625 = same as above → 34.34 ft²

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Problem 6: Sector with angle 90°, radius 12 m

This is a quarter circle.

Full area = 3.14 × 12² = 3.14 × 144 = 452.16
Quarter = 452.16 ÷ 4 = 113.04 m²

Or: (90/360) = 1/4 → same result.

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Problem 7: Sector with angle 120°, radius 6 ft

Fraction = 120/360 = 1/3
Full area = 3.14 × 6² = 3.14 × 36 = 113.04
Sector area = 113.04 ÷ 3 = 37.68 ft²

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Problem 8: Sector with angle 205°, radius 3 m

Fraction = 205/360
Simplify? Not necessary.
Full area = 3.14 × 3² = 3.14 × 9 = 28.26
Sector area = (205/360) × 28.26

Calculate:
205 ÷ 360 = 0.569444...
× 28.26 ≈ ?

Better:
(205 × 28.26) ÷ 360

First, 205 × 28.26
Breakdown:
200 × 28.26 = 5652
5 × 28.26 = 141.3
Total = 5652 + 141.3 = 5793.3

Now divide by 360:
5793.3 ÷ 360 = ?

360 × 16 = 5760
5793.3 - 5760 = 33.3
So 16 + 33.3/360 ≈ 16 + 0.0925 = 16.0925

Wait — that can’t be right because full circle is only 28.26, and 205° is more than half, so should be around 16? Actually yes, 205/360 is about 0.57, and 0.57 × 28.26 ≈ 16.1

Let me compute exactly:

205/360 = 41/72
41/72 × 28.26 = ?

First, 28.26 ÷ 72 = 0.3925
Then ×41 = 0.3925 × 40 = 15.7, plus 0.3925 = 16.0925 → 16.09 m² (rounded to two decimals)

Alternatively:
(205 × 3.14 × 9) / 360
= (205 × 28.26) / 360 = 5793.3 / 360 = 16.0925 → 16.09 m²

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Now compiling all answers:

1. 254.34 yd²
2. 2461.76 ft²
3. 98.47 m²
4. 4.27 yd²
5. 34.34 ft²
6. 113.04 m²
7. 37.68 ft²
8. 16.09 m²

Double-checking Problem 3:
5.6² = 31.36
3.14 × 31.36:
3 × 31.36 = 94.08
0.14 × 31.36 = 4.3904
Sum: 98.4704 → Yes, 98.47 when rounded.

Problem 8: 205/360 * 3.14 * 9 = (205*28.26)/360 = 5793.3/360 = 16.0925 → 16.09

All good.

Final Answer:
1. 254.34
2. 2461.76
3. 98.47
4. 4.27
5. 34.34
6. 113.04
7. 37.68
8. 16.09