Circle Worksheets - Math Monks - Free Printable
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Step-by-step solution for: Circle Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Circle Worksheets - Math Monks
Let’s solve each circle problem step by step. We’ll use π = 3.14 as instructed.
Remember these formulas:
- Diameter = 2 × Radius
- Radius = Diameter ÷ 2
- Area = π × Radius²
- Circumference = 2 × π × Radius (or π × Diameter)
We’ll go one by one.
---
Problem 1:
Radius = 4 cm
→ Diameter = 2 × 4 = 8 cm
→ Area = 3.14 × 4² = 3.14 × 16 = 50.24 cm²
→ Circumference = 2 × 3.14 × 4 = 6.28 × 4 = 25.12 cm
---
Problem 2:
Diameter = 12 m
→ Radius = 12 ÷ 2 = 6 m
→ Area = 3.14 × 6² = 3.14 × 36 = 113.04 m²
→ Circumference = 3.14 × 12 = 37.68 m
---
Problem 3:
Radius = 7 ft
→ Diameter = 2 × 7 = 14 ft
→ Area = 3.14 × 7² = 3.14 × 49 = 153.86 ft²
→ Circumference = 2 × 3.14 × 7 = 6.28 × 7 = 43.96 ft
---
Problem 4:
Radius = 22 in
→ Diameter = 2 × 22 = 44 in
→ Area = 3.14 × 22² = 3.14 × 484 = let’s calculate:
3 × 484 = 1452, 0.14 × 484 = 67.76 → total = 1452 + 67.76 = 1519.76 in²
→ Circumference = 2 × 3.14 × 22 = 6.28 × 22 =
6 × 22 = 132, 0.28 × 22 = 6.16 → total = 132 + 6.16 = 138.16 in
---
Problem 5:
Radius = 17.5 ft
→ Diameter = 2 × 17.5 = 35 ft
→ Area = 3.14 × (17.5)²
First, 17.5² = 306.25
Then, 3.14 × 306.25 =
3 × 306.25 = 918.75
0.14 × 306.25 = 42.875
Total = 918.75 + 42.875 = 961.625 ft²
→ Circumference = 2 × 3.14 × 17.5 = 6.28 × 17.5
6 × 17.5 = 105, 0.28 × 17.5 = 4.9 → total = 105 + 4.9 = 109.9 ft
---
Problem 6:
Diameter = 33 m
→ Radius = 33 ÷ 2 = 16.5 m
→ Area = 3.14 × (16.5)²
16.5² = 272.25
3.14 × 272.25 =
3 × 272.25 = 816.75
0.14 × 272.25 = 38.115
Total = 816.75 + 38.115 = 854.865 m²
→ Circumference = 3.14 × 33 =
3 × 33 = 99, 0.14 × 33 = 4.62 → total = 99 + 4.62 = 103.62 m
---
Problem 7:
Radius = 11.5 ft
→ Diameter = 2 × 11.5 = 23 ft
→ Area = 3.14 × (11.5)²
11.5² = 132.25
3.14 × 132.25 =
3 × 132.25 = 396.75
0.14 × 132.25 = 18.515
Total = 396.75 + 18.515 = 415.265 ft²
→ Circumference = 2 × 3.14 × 11.5 = 6.28 × 11.5
6 × 11.5 = 69, 0.28 × 11.5 = 3.22 → total = 69 + 3.22 = 72.22 ft
---
Problem 8:
Radius = 48 mm
→ Diameter = 2 × 48 = 96 mm
→ Area = 3.14 × 48²
48² = 2304
3.14 × 2304 =
3 × 2304 = 6912
0.14 × 2304 = 322.56
Total = 6912 + 322.56 = 7234.56 mm²
→ Circumference = 2 × 3.14 × 48 = 6.28 × 48
6 × 48 = 288, 0.28 × 48 = 13.44 → total = 288 + 13.44 = 301.44 mm
---
Final Answer:
1. Diameter = 8 cm, Area = 50.24 cm², Circumference = 25.12 cm
2. Radius = 6 m, Area = 113.04 m², Circumference = 37.68 m
3. Diameter = 14 ft, Area = 153.86 ft², Circumference = 43.96 ft
4. Diameter = 44 in, Area = 1519.76 in², Circumference = 138.16 in
5. Diameter = 35 ft, Area = 961.625 ft², Circumference = 109.9 ft
6. Radius = 16.5 m, Area = 854.865 m², Circumference = 103.62 m
7. Diameter = 23 ft, Area = 415.265 ft², Circumference = 72.22 ft
8. Diameter = 96 mm, Area = 7234.56 mm², Circumference = 301.44 mm
Remember these formulas:
- Diameter = 2 × Radius
- Radius = Diameter ÷ 2
- Area = π × Radius²
- Circumference = 2 × π × Radius (or π × Diameter)
We’ll go one by one.
---
Problem 1:
Radius = 4 cm
→ Diameter = 2 × 4 = 8 cm
→ Area = 3.14 × 4² = 3.14 × 16 = 50.24 cm²
→ Circumference = 2 × 3.14 × 4 = 6.28 × 4 = 25.12 cm
---
Problem 2:
Diameter = 12 m
→ Radius = 12 ÷ 2 = 6 m
→ Area = 3.14 × 6² = 3.14 × 36 = 113.04 m²
→ Circumference = 3.14 × 12 = 37.68 m
---
Problem 3:
Radius = 7 ft
→ Diameter = 2 × 7 = 14 ft
→ Area = 3.14 × 7² = 3.14 × 49 = 153.86 ft²
→ Circumference = 2 × 3.14 × 7 = 6.28 × 7 = 43.96 ft
---
Problem 4:
Radius = 22 in
→ Diameter = 2 × 22 = 44 in
→ Area = 3.14 × 22² = 3.14 × 484 = let’s calculate:
3 × 484 = 1452, 0.14 × 484 = 67.76 → total = 1452 + 67.76 = 1519.76 in²
→ Circumference = 2 × 3.14 × 22 = 6.28 × 22 =
6 × 22 = 132, 0.28 × 22 = 6.16 → total = 132 + 6.16 = 138.16 in
---
Problem 5:
Radius = 17.5 ft
→ Diameter = 2 × 17.5 = 35 ft
→ Area = 3.14 × (17.5)²
First, 17.5² = 306.25
Then, 3.14 × 306.25 =
3 × 306.25 = 918.75
0.14 × 306.25 = 42.875
Total = 918.75 + 42.875 = 961.625 ft²
→ Circumference = 2 × 3.14 × 17.5 = 6.28 × 17.5
6 × 17.5 = 105, 0.28 × 17.5 = 4.9 → total = 105 + 4.9 = 109.9 ft
---
Problem 6:
Diameter = 33 m
→ Radius = 33 ÷ 2 = 16.5 m
→ Area = 3.14 × (16.5)²
16.5² = 272.25
3.14 × 272.25 =
3 × 272.25 = 816.75
0.14 × 272.25 = 38.115
Total = 816.75 + 38.115 = 854.865 m²
→ Circumference = 3.14 × 33 =
3 × 33 = 99, 0.14 × 33 = 4.62 → total = 99 + 4.62 = 103.62 m
---
Problem 7:
Radius = 11.5 ft
→ Diameter = 2 × 11.5 = 23 ft
→ Area = 3.14 × (11.5)²
11.5² = 132.25
3.14 × 132.25 =
3 × 132.25 = 396.75
0.14 × 132.25 = 18.515
Total = 396.75 + 18.515 = 415.265 ft²
→ Circumference = 2 × 3.14 × 11.5 = 6.28 × 11.5
6 × 11.5 = 69, 0.28 × 11.5 = 3.22 → total = 69 + 3.22 = 72.22 ft
---
Problem 8:
Radius = 48 mm
→ Diameter = 2 × 48 = 96 mm
→ Area = 3.14 × 48²
48² = 2304
3.14 × 2304 =
3 × 2304 = 6912
0.14 × 2304 = 322.56
Total = 6912 + 322.56 = 7234.56 mm²
→ Circumference = 2 × 3.14 × 48 = 6.28 × 48
6 × 48 = 288, 0.28 × 48 = 13.44 → total = 288 + 13.44 = 301.44 mm
---
Final Answer:
1. Diameter = 8 cm, Area = 50.24 cm², Circumference = 25.12 cm
2. Radius = 6 m, Area = 113.04 m², Circumference = 37.68 m
3. Diameter = 14 ft, Area = 153.86 ft², Circumference = 43.96 ft
4. Diameter = 44 in, Area = 1519.76 in², Circumference = 138.16 in
5. Diameter = 35 ft, Area = 961.625 ft², Circumference = 109.9 ft
6. Radius = 16.5 m, Area = 854.865 m², Circumference = 103.62 m
7. Diameter = 23 ft, Area = 415.265 ft², Circumference = 72.22 ft
8. Diameter = 96 mm, Area = 7234.56 mm², Circumference = 301.44 mm
Parent Tip: Review the logic above to help your child master the concept of circle review worksheet.
