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

Let’s solve each circle problem step by step. We’ll use:

- Circumference (C) = 2 × π × r
- Area (A) = π × r²
- Use π = 3.14

Remember:
→ If you’re given the radius (r), plug it directly into the formulas.
→ If you’re given the diameter (d), divide by 2 to get the radius first: r = d ÷ 2.

---

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

---

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

---

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

---

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

---

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

---

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 754.39 ft² (if needed, but we’ll keep as is for now)

Wait — let’s calculate that again carefully:
15.5 × 15.5 = 240.25
3.14 × 240.25 = Let’s do 3 × 240.25 = 720.75, and 0.14 × 240.25 = 33.635 → Total = 720.75 + 33.635 = 754.385 → So 754.39 ft² if rounding to two decimals. But since others are exact, maybe leave as 754.385? Actually, let’s check instructions — they don’t specify rounding, so we can write full value or round reasonably. I’ll go with 754.39 ft² for consistency with decimal places.

Actually, looking at other answers, many have 2 decimals. So yes, 754.39 ft²

But wait — 3.14 × 240.25:

Breakdown:
240.25 × 3 = 720.75
240.25 × 0.14 = 240.25 × 14 / 100 = (240.25 × 10 = 2402.5; 240.25 × 4 = 961 → total 2402.5 + 961 = 3363.5 → divided by 100 = 33.635)
So 720.75 + 33.635 = 754.385 → which rounds to 754.39

Okay.

---

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 × 15.25 = 91.5, 0.28 × 15.25 = ?
0.28 × 15 = 4.2, 0.28 × 0.25 = 0.07 → total 4.27 → so 91.5 + 4.27 = 95.77 m

Better way: 6.28 × 15.25
= 6.28 × (15 + 0.25) = 6.28×15 = 94.2, 6.28×0.25 = 1.57 → total 94.2 + 1.57 = 95.77 m

Area: A = 3.14 × (15.25)²
First, 15.25² = 15.25 × 15.25
= (15 + 0.25)² = 15² + 2×15×0.25 + 0.25² = 225 + 7.5 + 0.0625 = 232.5625
Now, 3.14 × 232.5625
= 3 × 232.5625 = 697.6875
0.14 × 232.5625 = let’s compute: 0.1 × 232.5625 = 23.25625, 0.04 × 232.5625 = 9.3025 → total 23.25625 + 9.3025 = 32.55875
Add: 697.6875 + 32.55875 = 730.24625 m² → Round to 730.25 m²

---

Problem 8: Radius = 3.5 km
C = 2 × 3.14 × 3.5 = 6.28 × 3.5
6 × 3.5 = 21, 0.28 × 3.5 = 0.98 → total 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 38.465 km² → Round to 38.47 km²

Wait — 3.14 × 12.25:
12.25 × 3 = 36.75
12.25 × 0.14 = 12.25 × 14 / 100 = (12.25 × 10 = 122.5; 12.25 × 4 = 49 → total 171.5 → /100 = 1.715)
So 36.75 + 1.715 = 38.465 → which is 38.47 km² when rounded to two decimals.

---

Now let’s compile all final answers neatly.

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