Math worksheet for calculating the area and circumference of circles with given radii and diameters.

Let's solve each problem step by step using the formulas for area and circumference of a circle:

🔷 Formulas:

- Area of a circle:
$$
A = \pi r^2
$$
- Circumference of a circle:
$$
C = 2\pi r \quad \text{or} \quad C = \pi d
$$
- Use $ \pi = 3.14 $

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We are given either the radius (r) or diameter (d) in each case.

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🔹 Problem 1:

- Radius $ r = 4.5 $ yd

Area:
$$
A = 3.14 \times (4.5)^2 = 3.14 \times 20.25 = 63.585 \, \text{yd}^2
$$

Circumference:
$$
C = 2 \times 3.14 \times 4.5 = 28.26 \, \text{yd}
$$

✔ Answer: Area = 63.585 yd², Circumference = 28.26 yd

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🔹 Problem 2:

- Radius $ r = 0.8 $ m

Area:
$$
A = 3.14 \times (0.8)^2 = 3.14 \times 0.64 = 2.0096 \, \text{m}^2
$$

Circumference:
$$
C = 2 \times 3.14 \times 0.8 = 5.024 \, \text{m}
$$

✔ Answer: Area = 2.0096 m², Circumference = 5.024 m

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🔹 Problem 3:

- Radius $ r = 3.8 $ yd

Area:
$$
A = 3.14 \times (3.8)^2 = 3.14 \times 14.44 = 45.3616 \, \text{yd}^2
$$

Circumference:
$$
C = 2 \times 3.14 \times 3.8 = 23.864 \, \text{yd}
$$

✔ Answer: Area = 45.3616 yd², Circumference = 23.864 yd

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🔹 Problem 4:

- Radius $ r = 4.4 $ m

Area:
$$
A = 3.14 \times (4.4)^2 = 3.14 \times 19.36 = 60.7744 \, \text{m}^2
$$

Circumference:
$$
C = 2 \times 3.14 \times 4.4 = 27.632 \, \text{m}
$$

✔ Answer: Area = 60.7744 m², Circumference = 27.632 m

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🔹 Problem 5:

- Radius $ r = 5.4 $ yd

Area:
$$
A = 3.14 \times (5.4)^2 = 3.14 \times 29.16 = 91.5624 \, \text{yd}^2
$$

Circumference:
$$
C = 2 \times 3.14 \times 5.4 = 33.912 \, \text{yd}
$$

✔ Answer: Area = 91.5624 yd², Circumference = 33.912 yd

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🔹 Problem 6:

- Radius $ r = 6.6 $ m

Area:
$$
A = 3.14 \times (6.6)^2 = 3.14 \times 43.56 = 136.6344 \, \text{m}^2
$$

Circumference:
$$
C = 2 \times 3.14 \times 6.6 = 41.448 \, \text{m}
$$

✔ Answer: Area = 136.6344 m², Circumference = 41.448 m

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🔹 Problem 7:

- Diameter $ d = 9.9 $ yd → Radius $ r = \frac{9.9}{2} = 4.95 $ yd

Area:
$$
A = 3.14 \times (4.95)^2 = 3.14 \times 24.5025 = 76.96735 \, \text{yd}^2
$$

Circumference:
$$
C = 3.14 \times 9.9 = 31.086 \, \text{yd}
$$

✔ Answer: Area = 76.967 yd², Circumference = 31.086 yd

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🔹 Problem 8:

- Diameter $ d = 11.5 $ in → Radius $ r = \frac{11.5}{2} = 5.75 $ in

Area:
$$
A = 3.14 \times (5.75)^2 = 3.14 \times 33.0625 = 103.81925 \, \text{in}^2
$$

Circumference:
$$
C = 3.14 \times 11.5 = 36.11 \, \text{in}
$$

✔ Answer: Area = 103.819 in², Circumference = 36.11 in

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✔ Final Answers Summary:

| # | Radius/Diameter | Area | Circumference |
|---|------------------|------|---------------|
| 1 | 4.5 yd | 63.585 yd² | 28.26 yd |
| 2 | 0.8 m | 2.0096 m² | 5.024 m |
| 3 | 3.8 yd | 45.3616 yd² | 23.864 yd |
| 4 | 4.4 m | 60.7744 m² | 27.632 m |
| 5 | 5.4 yd | 91.5624 yd² | 33.912 yd |
| 6 | 6.6 m | 136.6344 m² | 41.448 m |
| 7 | 9.9 yd (d) | 76.967 yd² | 31.086 yd |
| 8 | 11.5 in (d) | 103.819 in² | 36.11 in |

> 📝 Note: All answers are rounded to 3–4 decimal places where appropriate.

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