Circumference and Area of a Circle Worksheet - Math Monks - Free Printable

Let’s solve each circle problem step by step.

We are told to use π = 3.14
Formulas:
Circumference (C) = 2πr
Area (A) = πr²

Note: If the diagram shows a diameter, remember radius r = diameter ÷ 2

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Problem 1:
Radius = 40 ft
C = 2 × 3.14 × 40 = 6.28 × 40 = 251.2 ft
A = 3.14 × 40² = 3.14 × 1600 = 5024 ft²

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Problem 2:
Diameter = 56 cm → Radius = 56 ÷ 2 = 28 cm
C = 2 × 3.14 × 28 = 6.28 × 28 = 175.84 cm
A = 3.14 × 28² = 3.14 × 784 = 2461.76 cm²

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Problem 3:
Radius = 62 in
C = 2 × 3.14 × 62 = 6.28 × 62 = 389.36 in
A = 3.14 × 62² = 3.14 × 3844 = 12070.16 in²

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Problem 4:
Radius = 12 cm
C = 2 × 3.14 × 12 = 6.28 × 12 = 75.36 cm
A = 3.14 × 12² = 3.14 × 144 = 452.16 cm²

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Problem 5:
Diameter = 102 mm → Radius = 102 ÷ 2 = 51 mm
C = 2 × 3.14 × 51 = 6.28 × 51 = 320.28 mm
A = 3.14 × 51² = 3.14 × 2601 = 8167.14 mm²

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Problem 6:
Radius = 15.5 ft
C = 2 × 3.14 × 15.5 = 6.28 × 15.5 = 97.34 ft
A = 3.14 × 15.5² = 3.14 × 240.25 = 754.385 ft² → Round to two decimals? Let’s keep as is or round to 754.39? But since inputs had one decimal, maybe keep one? Wait — original says “use π=3.14” so we’ll compute exactly with that.

Actually, let’s recalculate A carefully:
15.5 × 15.5 = 240.25
3.14 × 240.25 =
Break it down:
3 × 240.25 = 720.75
0.14 × 240.25 = 33.635
Total = 720.75 + 33.635 = 754.385 ft² → We can write as 754.39 ft² if rounding to hundredths, but since others didn’t specify, I’ll leave as 754.385? Actually, looking at other problems, they likely expect exact calculation with 3.14 and no extra rounding unless needed. But for consistency, let’s check Problem 8 later — actually, let’s just report what we get.

Wait — in school worksheets, usually they expect you to multiply and report full result from 3.14. So 754.385 is fine, but perhaps write as 754.39? Hmm. Let me see standard practice — since 3.14 has 3 sig figs, but measurements vary. To be safe, I’ll report as calculated: 754.385 → but maybe the worksheet expects rounded to two decimals? Looking at Problem 7 and 8, they have decimals too. Let’s do all consistently to two decimal places where needed.

Actually, let’s recompute all areas and circumferences using calculator-style precision with 3.14 and report final answers as numbers without over-rounding intermediate steps.

But for simplicity and matching typical worksheet expectations, I’ll report:

C = 97.34 ft (exact: 6.28 * 15.5 = 97.34)
A = 3.14 * 240.25 = let's compute again:
3.14 * 240 = 753.6
3.14 * 0.25 = 0.785
Total = 753.6 + 0.785 = 754.385 → so 754.39 ft² if rounded to nearest hundredth. But many worksheets accept 754.385. However, to match format of others which may not show trailing zeros, I'll use 754.39.

Wait — actually, let’s look back: Problem 1 gave 5024 which is integer, Problem 2 gave 2461.76 — so they are keeping two decimals when needed. So for consistency, I’ll use two decimal places for all non-integer results.

So for Problem 6:
A = 754.39 ft² (rounded)

But let’s confirm: 3.14 × 240.25
Do 314 × 24025 / 10000
Easier: 3.14 × 240.25 = (3 + 0.14) × 240.25 = 720.75 + 33.635 = 754.385 → yes. So 754.39 if rounded to two decimals.

I think it’s safer to report as 754.39 ft².

Similarly, C was 97.34 — exact.

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Problem 7:
Diameter = 30.5 m → Radius = 30.5 ÷ 2 = 15.25 m
C = 2 × 3.14 × 15.25 = 6.28 × 15.25
Calculate: 6.28 × 15 = 94.2, 6.28 × 0.25 = 1.57 → Total = 94.2 + 1.57 = 95.77 m
A = 3.14 × (15.25)²
First, 15.25² = 232.5625
Then 3.14 × 232.5625
Compute: 3 × 232.5625 = 697.6875
0.14 × 232.5625 = 32.55875
Total = 697.6875 + 32.55875 = 730.24625 m² → Round to two decimals: 730.25 m²

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Problem 8:
Radius = 3.5 km
C = 2 × 3.14 × 3.5 = 6.28 × 3.5 = 21.98 km
A = 3.14 × (3.5)² = 3.14 × 12.25
3 × 12.25 = 36.75
0.14 × 12.25 = 1.715
Total = 36.75 + 1.715 = 38.465 km² → Round to two decimals: 38.47 km²

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Now compiling all answers:

Final Answer:
1. C = 251.2 ft, A = 5024 ft²
2. C = 175.84 cm, A = 2461.76 cm²
3. C = 389.36 in, A = 12070.16 in²
4. C = 75.36 cm, A = 452.16 cm²
5. C = 320.28 mm, A = 8167.14 mm²
6. C = 97.34 ft, A = 754.39 ft²
7. C = 95.77 m, A = 730.25 m²
8. C = 21.98 km, A = 38.47 km²