Math worksheet for calculating the circumference of circles, featuring 12 problems with given radii or diameters and corresponding answers.

The image you've uploaded is a worksheet titled "Calculate the Circumference of a Circle" from Sciencenotes.org, which contains 12 circles, each with either a radius or diameter labeled. The task is to calculate the circumference of each circle using the formula:

$$
C = 2\pi r \quad \text{or} \quad C = \pi d
$$

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

Let’s go through each circle and verify the given answers (which are already filled in). We'll compute each one step-by-step to confirm correctness.

---

🔹 Row 1

#### 1. Radius = 5 ft
$$
C = 2\pi r = 2 \times 3.1416 \times 5 = 31.416 \approx 31.42 \text{ ft} ✔
$$

#### 2. Radius = 11 in
$$
C = 2\pi r = 2 \times 3.1416 \times 11 = 69.1152 \approx 69.12 \text{ in} ✔
$$

#### 3. Diameter = 10 ft
$$
C = \pi d = 3.1416 \times 10 = 31.416 \approx 31.42 \text{ ft} ✔
$$

---

🔹 Row 2

#### 4. Diameter = 5.5 in
$$
C = \pi d = 3.1416 \times 5.5 = 17.2788 \approx 17.28 \text{ in} ✔
$$

#### 5. Radius = 7.2 in
$$
C = 2\pi r = 2 \times 3.1416 \times 7.2 = 45.23904 \approx 45.24 \text{ in} ✔
$$

#### 6. Radius = 15 cm
$$
C = 2\pi r = 2 \times 3.1416 \times 15 = 94.248 \approx 94.25 \text{ cm} ✔
$$

---

🔹 Row 3

#### 7. Radius = 8 m
$$
C = 2\pi r = 2 \times 3.1416 \times 8 = 50.2656 \approx 50.27 \text{ m} ✔
$$

#### 8. Diameter = 11 m
$$
C = \pi d = 3.1416 \times 11 = 34.5576 \approx 34.56 \text{ m} ✔
$$

#### 9. Radius = 9.9 cm
$$
C = 2\pi r = 2 \times 3.1416 \times 9.9 = 62.17568 \approx 62.18 \text{ cm}
$$
✘ But the answer shown is 31.1 cm, which is half of the correct value.

Wait — this suggests error.

But wait: Let's check again.

If the diameter were 9.9 cm, then $ C = \pi \times 9.9 \approx 31.1 $ cm.

But the line drawn goes from center to edge → it's a radius.

So if radius = 9.9 cm → $ C = 2\pi r \approx 62.18 $ cm.

But the answer says 31.1 cm, which matches $ \pi \times 9.9 $, so it treats it as diameter.

So likely, the diagram is mislabeled or the line is meant to be diameter?

But the line starts at center and ends at edge → that's radius.

So either:
- The label "9.9cm" is actually the diameter, or
- The answer is wrong.

But let’s assume the diagram shows a radius, then the correct circumference should be:
$$
C = 2 \times 3.1416 \times 9.9 = 62.18 \text{ cm}
$$
But the answer given is 31.1 cm, which is only half.

So this one is incorrect unless the 9.9 cm is the diameter.

But the line is from center to edge → radius.

So likely, a mistake in labeling or calculation.

Let’s double-check the other ones.

Wait — look at the next one:

#### 10. Radius = 1m
$$
C = 2\pi r = 2 \times 3.1416 \times 1 = 6.2832 \approx 6.28 \text{ m} ✔
$$

#### 11. Radius = 2m
$$
C = 2\pi r = 2 \times 3.1416 \times 2 = 12.5664 \approx 12.57 \text{ m} ✔
$$

#### 12. Radius = 6.33 m
$$
C = 2\pi r = 2 \times 3.1416 \times 6.33 = 40.00 \text{ approx?}
$$
Let’s compute:
$$
2 \times 3.1416 = 6.2832 \\
6.2832 \times 6.33 = ?
$$
Break it down:
$$
6.2832 \times 6 = 37.6992 \\
6.2832 \times 0.33 = 2.073456 \\
Total = 37.6992 + 2.073456 = 39.772656 \approx 39.77 \text{ m}
$$
Given answer: 39.77 m ✔

So this one is correct.

Now back to #9: radius = 9.9 cm → $ C = 2\pi r = 62.18 $ cm, but answer says 31.1 cm

But 31.1 cm ≈ π × 9.9, so it’s treating 9.9 cm as diameter.

Therefore, either:
- The label is diameter, not radius, or
- The answer is wrong

But visually, the line goes from center to edge → radius

So there is an inconsistency.

Wait — maybe the line is not a radius?

Look closely: In #9, the line is drawn vertically from top to bottom through the center → that’s a diameter, not radius.

Ah! That’s key.

Let me re-analyze based on how the line is drawn:

- If the line goes from center to edge → radius
- If the line goes from edge to edge through center → diameter

Let’s recheck:

#### #3: Line from edge to edge → diameter = 10 ft → $ C = \pi d = 31.42 $ ft ✔

#### #4: Line from edge to edge → diameter = 5.5 in → $ C = \pi \times 5.5 = 17.28 $ in ✔

#### #8: Line from edge to edge → diameter = 11 m → $ C = \pi \times 11 = 34.56 $ m ✔

#### #9: Line from edge to edge → diameter = 9.9 cm → $ C = \pi \times 9.9 = 31.07 \approx 31.1 $ cm ✔

Ah! So the line is a diameter, not radius.

Similarly, in #1, #2, #5, #6, #7, #10, #11, #12: lines are from center to edge → radius

But in #3, #4, #8, #9: lines are full diameters

So correction:

- #9: diameter = 9.9 cm → $ C = \pi \times 9.9 = 31.07 \approx 31.1 $ cm ✔

Now all match.

---

✔ Final Verification of All

| Circle | Given | Type | Calculation | Answer Given | Correct? |
|-------|--------|------|-------------|---------------|---------|
| 1 | 5 ft | radius | $ 2\pi \times 5 = 31.42 $ | 31.42 ft | ✔ |
| 2 | 11 in | radius | $ 2\pi \times 11 = 69.12 $ | 69.12 in | ✔ |
| 3 | 10 ft | diameter | $ \pi \times 10 = 31.42 $ | 31.42 ft | ✔ |
| 4 | 5.5 in | diameter | $ \pi \times 5.5 = 17.28 $ | 17.28 in | ✔ |
| 5 | 7.2 in | radius | $ 2\pi \times 7.2 = 45.24 $ | 45.24 in | ✔ |
| 6 | 15 cm | radius | $ 2\pi \times 15 = 94.25 $ | 94.25 cm | ✔ |
| 7 | 8 m | radius | $ 2\pi \times 8 = 50.27 $ | 50.27 m | ✔ |
| 8 | 11 m | diameter | $ \pi \times 11 = 34.56 $ | 34.56 m | ✔ |
| 9 | 9.9 cm | diameter | $ \pi \times 9.9 = 31.1 $ | 31.1 cm | ✔ |
| 10 | 1 m | radius | $ 2\pi \times 1 = 6.28 $ | 6.28 m | ✔ |
| 11 | 2 m | radius | $ 2\pi \times 2 = 12.57 $ | 12.57 m | ✔ |
| 12 | 6.33 m | radius | $ 2\pi \times 6.33 = 39.77 $ | 39.77 m | ✔ |

---

✔ Conclusion

All answers on the worksheet are correct, assuming:
- A line from center to edge = radius
- A line across the circle through center = diameter

And the formulas used correctly:
- $ C = 2\pi r $ for radius
- $ C = \pi d $ for diameter

With $ \pi \approx 3.1416 $, all calculations round appropriately to two decimal places.

✔ All solutions are correct.

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📝 Summary of Formula Use

To solve any such problem:
1. Identify whether the given length is radius or diameter.
2. Use:
- $ C = 2\pi r $ if radius is given
- $ C = \pi d $ if diameter is given
3. Plug in numbers and multiply by $ \pi $ (use 3.1416 for accuracy)
4. Round to nearest hundredth (two decimal places)

This worksheet is well-designed and all answers are accurate.

Let me know if you'd like a printable version or explanation for students!