Circumference of Circles worksheet with radius values for calculating circumference and area.
Worksheet titled "Circumference of Circles" with nine circles, each labeled with a radius in centimeters, asking students to calculate circumference and area.
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Step-by-step solution for: Circumference of Circles cm Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Circumference of Circles cm Worksheets
Let’s solve each circle problem step by step.
We are given the radius of each circle, and we need to find:
- The circumference: C = 2 × π × r
- The area: A = π × r²
We’ll use π ≈ 3.14 for all calculations (since it’s a school-level worksheet).
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Circumference = 2 × 3.14 × 44 = 6.28 × 44
→ 6 × 44 = 264, 0.28 × 44 = 12.32 → total = 276.32 cm
Area = 3.14 × 44² = 3.14 × 1936
→ 3 × 1936 = 5808, 0.14 × 1936 = 271.04 → total = 6079.04 cm²
✔ Check: 44² = 1936 ✔️; 3.14 × 1936 = let’s compute again:
1936 × 3 = 5808
1936 × 0.14 = 1936 × 14 / 100 = (1936×10=19360 + 1936×4=7744) = 27104 ÷ 100 = 271.04 → 5808 + 271.04 = 6079.04 ✔️
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C = 2 × 3.14 × 24 = 6.28 × 24
→ 6 × 24 = 144, 0.28 × 24 = 6.72 → total = 150.72 cm
A = 3.14 × 24² = 3.14 × 576
→ 3 × 576 = 1728, 0.14 × 576 = 80.64 → total = 1808.64 cm²
Check: 24² = 576 ✔️; 3.14 × 576:
576 × 3 = 1728
576 × 0.14 = 576 × 14 / 100 = (576×10=5760 + 576×4=2304) = 8064 ÷ 100 = 80.64 → 1728 + 80.64 = 1808.64 ✔️
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C = 2 × 3.14 × 33 = 6.28 × 33
→ 6 × 33 = 198, 0.28 × 33 = 9.24 → total = 207.24 cm
A = 3.14 × 33² = 3.14 × 1089
→ 3 × 1089 = 3267, 0.14 × 1089 = 152.46 → total = 3419.46 cm²
Check: 33² = 1089 ✔️; 3.14 × 1089:
1089 × 3 = 3267
1089 × 0.14 = 1089 × 14 / 100 = (1089×10=10890 + 1089×4=4356) = 15246 ÷ 100 = 152.46 → 3267 + 152.46 = 3419.46 ✔️
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C = 2 × 3.14 × 16 = 6.28 × 16
→ 6 × 16 = 96, 0.28 × 16 = 4.48 → total = 100.48 cm
A = 3.14 × 16² = 3.14 × 256
→ 3 × 256 = 768, 0.14 × 256 = 35.84 → total = 803.84 cm²
Check: 16² = 256 ✔️; 3.14 × 256:
256 × 3 = 768
256 × 0.14 = 256 × 14 / 100 = (256×10=2560 + 256×4=1024) = 3584 ÷ 100 = 35.84 → 768 + 35.84 = 803.84 ✔️
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C = 2 × 3.14 × 5 = 6.28 × 5 = 31.4 cm
A = 3.14 × 5² = 3.14 × 25 = 78.5 cm²
Easy check: 5² = 25 ✔️; 3.14 × 25 = 78.5 ✔️
---
C = 2 × 3.14 × 7 = 6.28 × 7 = 43.96 cm
A = 3.14 × 7² = 3.14 × 49
→ 3 × 49 = 147, 0.14 × 49 = 6.86 → total = 153.86 cm²
Check: 7² = 49 ✔️; 3.14 × 49:
49 × 3 = 147
49 × 0.14 = 49 × 14 / 100 = (49×10=490 + 49×4=196) = 686 ÷ 100 = 6.86 → 147 + 6.86 = 153.86 ✔️
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C = 2 × 3.14 × 37 = 6.28 × 37
Breakdown: 6 × 37 = 222, 0.28 × 37 = ?
0.28 × 30 = 8.4, 0.28 × 7 = 1.96 → total 10.36 → so C = 222 + 10.36 = 232.36 cm
A = 3.14 × 37² = 3.14 × 1369
First, 37² = 1369 ✔️
Now 3.14 × 1369:
3 × 1369 = 4107
0.14 × 1369 = 1369 × 14 / 100
1369 × 10 = 13690
1369 × 4 = 5476
Sum = 13690 + 5476 = 19166 → ÷100 = 191.66
Total area = 4107 + 191.66 = 4298.66 cm²
Double-check circumference: 6.28 × 37
Alternative: 6.28 × 30 = 188.4, 6.28 × 7 = 43.96 → 188.4 + 43.96 = 232.36 ✔️
---
C = 2 × 3.14 × 9 = 6.28 × 9 = 56.52 cm
A = 3.14 × 9² = 3.14 × 81
→ 3 × 81 = 243, 0.14 × 81 = 11.34 → total = 254.34 cm²
Check: 9² = 81 ✔️; 3.14 × 81:
81 × 3 = 243
81 × 0.14 = 81 × 14 / 100 = (81×10=810 + 81×4=324) = 1134 ÷ 100 = 11.34 → 243 + 11.34 = 254.34 ✔️
---
C = 2 × 3.14 × 25 = 6.28 × 25
→ 6 × 25 = 150, 0.28 × 25 = 7 → total = 157 cm
A = 3.14 × 25² = 3.14 × 625
→ 3 × 625 = 1875, 0.14 × 625 = 87.5 → total = 1962.5 cm²
Check: 25² = 625 ✔️; 3.14 × 625:
625 × 3 = 1875
625 × 0.14 = 625 × 14 / 100 = (625×10=6250 + 625×4=2500) = 8750 ÷ 100 = 87.5 → 1875 + 87.5 = 1962.5 ✔️
Also note: Circumference with r=25 is exactly 50π → 50 × 3.14 = 157 ✔️
---
All calculations verified.
Final Answer:
1. Circumference: 276.32 cm, Area: 6079.04 cm²
2. Circumference: 150.72 cm, Area: 1808.64 cm²
3. Circumference: 207.24 cm, Area: 3419.46 cm²
4. Circumference: 100.48 cm, Area: 803.84 cm²
5. Circumference: 31.4 cm, Area: 78.5 cm²
6. Circumference: 43.96 cm, Area: 153.86 cm²
7. Circumference: 232.36 cm, Area: 4298.66 cm²
8. Circumference: 56.52 cm, Area: 254.34 cm²
9. Circumference: 157 cm, Area: 1962.5 cm²
We are given the radius of each circle, and we need to find:
- The circumference: C = 2 × π × r
- The area: A = π × r²
We’ll use π ≈ 3.14 for all calculations (since it’s a school-level worksheet).
---
Circle 1: radius = 44 cm
Circumference = 2 × 3.14 × 44 = 6.28 × 44
→ 6 × 44 = 264, 0.28 × 44 = 12.32 → total = 276.32 cm
Area = 3.14 × 44² = 3.14 × 1936
→ 3 × 1936 = 5808, 0.14 × 1936 = 271.04 → total = 6079.04 cm²
✔ Check: 44² = 1936 ✔️; 3.14 × 1936 = let’s compute again:
1936 × 3 = 5808
1936 × 0.14 = 1936 × 14 / 100 = (1936×10=19360 + 1936×4=7744) = 27104 ÷ 100 = 271.04 → 5808 + 271.04 = 6079.04 ✔️
---
Circle 2: radius = 24 cm
C = 2 × 3.14 × 24 = 6.28 × 24
→ 6 × 24 = 144, 0.28 × 24 = 6.72 → total = 150.72 cm
A = 3.14 × 24² = 3.14 × 576
→ 3 × 576 = 1728, 0.14 × 576 = 80.64 → total = 1808.64 cm²
Check: 24² = 576 ✔️; 3.14 × 576:
576 × 3 = 1728
576 × 0.14 = 576 × 14 / 100 = (576×10=5760 + 576×4=2304) = 8064 ÷ 100 = 80.64 → 1728 + 80.64 = 1808.64 ✔️
---
Circle 3: radius = 33 cm
C = 2 × 3.14 × 33 = 6.28 × 33
→ 6 × 33 = 198, 0.28 × 33 = 9.24 → total = 207.24 cm
A = 3.14 × 33² = 3.14 × 1089
→ 3 × 1089 = 3267, 0.14 × 1089 = 152.46 → total = 3419.46 cm²
Check: 33² = 1089 ✔️; 3.14 × 1089:
1089 × 3 = 3267
1089 × 0.14 = 1089 × 14 / 100 = (1089×10=10890 + 1089×4=4356) = 15246 ÷ 100 = 152.46 → 3267 + 152.46 = 3419.46 ✔️
---
Circle 4: radius = 16 cm
C = 2 × 3.14 × 16 = 6.28 × 16
→ 6 × 16 = 96, 0.28 × 16 = 4.48 → total = 100.48 cm
A = 3.14 × 16² = 3.14 × 256
→ 3 × 256 = 768, 0.14 × 256 = 35.84 → total = 803.84 cm²
Check: 16² = 256 ✔️; 3.14 × 256:
256 × 3 = 768
256 × 0.14 = 256 × 14 / 100 = (256×10=2560 + 256×4=1024) = 3584 ÷ 100 = 35.84 → 768 + 35.84 = 803.84 ✔️
---
Circle 5: radius = 5 cm
C = 2 × 3.14 × 5 = 6.28 × 5 = 31.4 cm
A = 3.14 × 5² = 3.14 × 25 = 78.5 cm²
Easy check: 5² = 25 ✔️; 3.14 × 25 = 78.5 ✔️
---
Circle 6: radius = 7 cm
C = 2 × 3.14 × 7 = 6.28 × 7 = 43.96 cm
A = 3.14 × 7² = 3.14 × 49
→ 3 × 49 = 147, 0.14 × 49 = 6.86 → total = 153.86 cm²
Check: 7² = 49 ✔️; 3.14 × 49:
49 × 3 = 147
49 × 0.14 = 49 × 14 / 100 = (49×10=490 + 49×4=196) = 686 ÷ 100 = 6.86 → 147 + 6.86 = 153.86 ✔️
---
Circle 7: radius = 37 cm
C = 2 × 3.14 × 37 = 6.28 × 37
Breakdown: 6 × 37 = 222, 0.28 × 37 = ?
0.28 × 30 = 8.4, 0.28 × 7 = 1.96 → total 10.36 → so C = 222 + 10.36 = 232.36 cm
A = 3.14 × 37² = 3.14 × 1369
First, 37² = 1369 ✔️
Now 3.14 × 1369:
3 × 1369 = 4107
0.14 × 1369 = 1369 × 14 / 100
1369 × 10 = 13690
1369 × 4 = 5476
Sum = 13690 + 5476 = 19166 → ÷100 = 191.66
Total area = 4107 + 191.66 = 4298.66 cm²
Double-check circumference: 6.28 × 37
Alternative: 6.28 × 30 = 188.4, 6.28 × 7 = 43.96 → 188.4 + 43.96 = 232.36 ✔️
---
Circle 8: radius = 9 cm
C = 2 × 3.14 × 9 = 6.28 × 9 = 56.52 cm
A = 3.14 × 9² = 3.14 × 81
→ 3 × 81 = 243, 0.14 × 81 = 11.34 → total = 254.34 cm²
Check: 9² = 81 ✔️; 3.14 × 81:
81 × 3 = 243
81 × 0.14 = 81 × 14 / 100 = (81×10=810 + 81×4=324) = 1134 ÷ 100 = 11.34 → 243 + 11.34 = 254.34 ✔️
---
Circle 9: radius = 25 cm
C = 2 × 3.14 × 25 = 6.28 × 25
→ 6 × 25 = 150, 0.28 × 25 = 7 → total = 157 cm
A = 3.14 × 25² = 3.14 × 625
→ 3 × 625 = 1875, 0.14 × 625 = 87.5 → total = 1962.5 cm²
Check: 25² = 625 ✔️; 3.14 × 625:
625 × 3 = 1875
625 × 0.14 = 625 × 14 / 100 = (625×10=6250 + 625×4=2500) = 8750 ÷ 100 = 87.5 → 1875 + 87.5 = 1962.5 ✔️
Also note: Circumference with r=25 is exactly 50π → 50 × 3.14 = 157 ✔️
---
All calculations verified.
Final Answer:
1. Circumference: 276.32 cm, Area: 6079.04 cm²
2. Circumference: 150.72 cm, Area: 1808.64 cm²
3. Circumference: 207.24 cm, Area: 3419.46 cm²
4. Circumference: 100.48 cm, Area: 803.84 cm²
5. Circumference: 31.4 cm, Area: 78.5 cm²
6. Circumference: 43.96 cm, Area: 153.86 cm²
7. Circumference: 232.36 cm, Area: 4298.66 cm²
8. Circumference: 56.52 cm, Area: 254.34 cm²
9. Circumference: 157 cm, Area: 1962.5 cm²
Parent Tip: Review the logic above to help your child master the concept of circumference worksheet.
