Area and Circumference Worksheet | Cazoom Maths Worksheets - Free Printable

Let's solve each problem step by step.

We are asked to find the area (A) and circumference (P, or perimeter) of circles.
The formulas we'll use:

- Area of a circle:
$$
A = \pi r^2
$$

- Circumference of a circle:
$$
P = \pi d \quad \text{or} \quad P = 2\pi r
$$

Where:
- $ r $ is the radius,
- $ d $ is the diameter,
- $ \pi \approx 3.1416 $

We’ll give answers to 2 decimal places.

---

1) Diameter = 6 m

- Radius $ r = \frac{6}{2} = 3 $ m

Area:
$$
A = \pi r^2 = \pi \times 3^2 = \pi \times 9 \approx 3.1416 \times 9 = 28.27 \, \text{m}^2
$$

Circumference:
$$
P = \pi d = \pi \times 6 \approx 3.1416 \times 6 = 18.85 \, \text{m}
$$

✔ A = 28.27 m², P = 18.85 m

---

2) Diameter = 9 mm

- Radius $ r = \frac{9}{2} = 4.5 $ mm

Area:
$$
A = \pi r^2 = \pi \times (4.5)^2 = \pi \times 20.25 \approx 3.1416 \times 20.25 = 63.62 \, \text{mm}^2
$$

Circumference:
$$
P = \pi d = \pi \times 9 \approx 3.1416 \times 9 = 28.27 \, \text{mm}
$$

✔ A = 63.62 mm², P = 28.27 mm

---

3) Diameter = 3 km

- Radius $ r = \frac{3}{2} = 1.5 $ km

Area:
$$
A = \pi r^2 = \pi \times (1.5)^2 = \pi \times 2.25 \approx 3.1416 \times 2.25 = 7.07 \, \text{km}^2
$$

Circumference:
$$
P = \pi d = \pi \times 3 \approx 3.1416 \times 3 = 9.42 \, \text{km}
$$

✔ A = 7.07 km², P = 9.42 km

---

4) Diameter = 5.5 cm

- Radius $ r = \frac{5.5}{2} = 2.75 $ cm

Area:
$$
A = \pi r^2 = \pi \times (2.75)^2 = \pi \times 7.5625 \approx 3.1416 \times 7.5625 = 23.76 \, \text{cm}^2
$$

Circumference:
$$
P = \pi d = \pi \times 5.5 \approx 3.1416 \times 5.5 = 17.28 \, \text{cm}
$$

✔ A = 23.76 cm², P = 17.28 cm

---

5) Diameter = 9.2 km

- Radius $ r = \frac{9.2}{2} = 4.6 $ km

Area:
$$
A = \pi r^2 = \pi \times (4.6)^2 = \pi \times 21.16 \approx 3.1416 \times 21.16 = 66.45 \, \text{km}^2
$$

Circumference:
$$
P = \pi d = \pi \times 9.2 \approx 3.1416 \times 9.2 = 28.89 \, \text{km}
$$

✔ A = 66.45 km², P = 28.89 km

---

6) Diameter = 7.1 m

- Radius $ r = \frac{7.1}{2} = 3.55 $ m

Area:
$$
A = \pi r^2 = \pi \times (3.55)^2 = \pi \times 12.6025 \approx 3.1416 \times 12.6025 = 39.61 \, \text{m}^2
$$

Circumference:
$$
P = \pi d = \pi \times 7.1 \approx 3.1416 \times 7.1 = 22.00 \, \text{m}
$$

✔ A = 39.61 m², P = 22.00 m

---

7) Diameter = 250 mm

- Radius $ r = \frac{250}{2} = 125 $ mm

Area:
$$
A = \pi r^2 = \pi \times (125)^2 = \pi \times 15625 \approx 3.1416 \times 15625 = 49087.38 \, \text{mm}^2
$$

Circumference:
$$
P = \pi d = \pi \times 250 \approx 3.1416 \times 250 = 785.40 \, \text{mm}
$$

✔ A = 49087.38 mm², P = 785.40 mm

---

✔ Final Answers:

| Question | Area (A) | Circumference (P) |
|---------|------------------|--------------------|
| 1) | 28.27 m² | 18.85 m |
| 2) | 63.62 mm² | 28.27 mm |
| 3) | 7.07 km² | 9.42 km |
| 4) | 23.76 cm² | 17.28 cm |
| 5) | 66.45 km² | 28.89 km |
| 6) | 39.61 m² | 22.00 m |
| 7) | 49087.38 mm² | 785.40 mm |

> 💡 Note: For question 7, the area is large because it’s in square millimeters. You could convert to cm² if needed:
> $ 49087.38 \, \text{mm}^2 = 490.87 \, \text{cm}^2 $, but since the input was in mm, keep as mm².

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