Printable math worksheet for practicing radius and diameter calculations using circumference.

Let's solve the problems step by step.

---

Part A: Choose the correct choice

We use the formulas:

- Circumference (C) = π × diameter (d)
- Circumference (C) = 2π × radius (r)
- So, diameter (d) = C / π
- And radius (r) = C / (2π)

We'll use π ≈ 3.14 or keep it as π for exact values.

---

#### 1) A circle has a circumference of 12π cm. What is the diameter?

Use:
$$ d = \frac{C}{\pi} = \frac{12\pi}{\pi} = 12 \text{ cm} $$

✔ Answer: a) 12 cm

---

#### 2) A wire of length 28π m is bent to form a circle. What is the radius?

Circumference = 28π m
So:
$$
C = 2\pi r \Rightarrow 28\pi = 2\pi r \Rightarrow r = \frac{28\pi}{2\pi} = 14 \text{ m}
$$

✔ Answer: c) 14 m

---

#### 3) A circular park has a circumference of 36π ft. Find its diameter.

$$
d = \frac{C}{\pi} = \frac{36\pi}{\pi} = 36 \text{ ft}
$$

✔ Answer: b) 36 ft

---

#### 4) The tip of the minute-hand travels 22π cm in one hour. Find the length of the minute-hand.

In one hour, the minute-hand completes one full revolution → so the distance traveled is the circumference of the circle traced by the tip.

So:
$$
C = 22\pi = 2\pi r \Rightarrow r = \frac{22\pi}{2\pi} = 11 \text{ cm}
$$

The length of the minute-hand is the radius.

✔ Answer: a) 11 cm

---

#### 5) The circumference of a bicycle wheel is 6π in. Find the diameter.

$$
d = \frac{C}{\pi} = \frac{6\pi}{\pi} = 6 \text{ in}
$$

✔ Answer: b) 6 in

---

Part B: Find the radius and diameter in each question

We’ll use:

- $ r = \frac{C}{2\pi} $
- $ d = \frac{C}{\pi} $

Let’s compute each row.

---

#### 5. Circumference = ? — Missing value. Probably typo or incomplete.

But let’s assume it’s missing, so we skip or note that data is missing.

Wait — looking at the table:

| S.No | Circumference | Radius | Diameter |
|------|---------------|--------|----------|
| 6. | 10π ft | | |
| 7. | 24π in | | |
| 8. | 34π m | | |
| 9. | 40π cm | | |
| 10. | 16π mm | | |

So we can solve all from 6 to 10.

---

#### 6. Circumference = 10π ft

- Radius:
$$
r = \frac{10\pi}{2\pi} = 5 \text{ ft}
$$
- Diameter:
$$
d = \frac{10\pi}{\pi} = 10 \text{ ft}
$$

✔ Radius: 5 ft, Diameter: 10 ft

---

#### 7. Circumference = 24π in

- Radius:
$$
r = \frac{24\pi}{2\pi} = 12 \text{ in}
$$
- Diameter:
$$
d = \frac{24\pi}{\pi} = 24 \text{ in}
$$

✔ Radius: 12 in, Diameter: 24 in

---

#### 8. Circumference = 34π m

- Radius:
$$
r = \frac{34\pi}{2\pi} = 17 \text{ m}
$$
- Diameter:
$$
d = \frac{34\pi}{\pi} = 34 \text{ m}
$$

✔ Radius: 17 m, Diameter: 34 m

---

#### 9. Circumference = 40π cm

- Radius:
$$
r = \frac{40\pi}{2\pi} = 20 \text{ cm}
$$
- Diameter:
$$
d = \frac{40\pi}{\pi} = 40 \text{ cm}
$$

✔ Radius: 20 cm, Diameter: 40 cm

---

#### 10. Circumference = 16π mm

- Radius:
$$
r = \frac{16\pi}{2\pi} = 8 \text{ mm}
$$
- Diameter:
$$
d = \frac{16\pi}{\pi} = 16 \text{ mm}
$$

✔ Radius: 8 mm, Diameter: 16 mm

---

✔ Final Answers:

---

Part A: Multiple Choice

1) a) 12 cm
2) c) 14 m
3) b) 36 ft
4) a) 11 cm
5) b) 6 in

---

Part B: Fill in the Table

| S.No | Circumference | Radius | Diameter |
|------|----------------|------------|-------------|
| 6. | 10π ft | 5 ft | 10 ft |
| 7. | 24π in | 12 in | 24 in |
| 8. | 34π m | 17 m | 34 m |
| 9. | 40π cm | 20 cm | 40 cm |
| 10. | 16π mm | 8 mm | 16 mm |

---

Let me know if you'd like this formatted as a printable answer sheet!