Let's solve the problem step by step.
We are given a worksheet asking to
calculate the circumference and area of each circle, with the radius (or diameter) provided for each circle.
---
🔷 Formulas:
-
Circumference of a circle:
$$
C = 2\pi r
$$
-
Area of a circle:
$$
A = \pi r^2
$$
Where:
- $ r $ is the
radius of the circle,
- $ \pi \approx 3.14 $ (we'll use this approximation unless otherwise specified).
> ⚠️ Note: In all the circles shown, the labeled line goes from the center to the edge — so these are
radii, not diameters.
---
Let’s go through each circle:
---
1. Radius = 12 cm
- Circumference:
$ C = 2 \times 3.14 \times 12 = 75.36 $ cm
- Area:
$ A = 3.14 \times 12^2 = 3.14 \times 144 = 452.16 $ cm²
✔ C = 75.36 cm, A = 452.16 cm²
---
2. Radius = 8 cm
- $ C = 2 \times 3.14 \times 8 = 50.24 $ cm
- $ A = 3.14 \times 8^2 = 3.14 \times 64 = 200.96 $ cm²
✔ C = 50.24 cm, A = 200.96 cm²
---
3. Radius = 19 cm
- $ C = 2 \times 3.14 \times 19 = 119.32 $ cm
- $ A = 3.14 \times 19^2 = 3.14 \times 361 = 1133.54 $ cm²
✔ C = 119.32 cm, A = 1133.54 cm²
---
4. Radius = 9 cm
- $ C = 2 \times 3.14 \times 9 = 56.52 $ cm
- $ A = 3.14 \times 9^2 = 3.14 \times 81 = 254.34 $ cm²
✔ C = 56.52 cm, A = 254.34 cm²
---
5. Radius = 5 cm
- $ C = 2 \times 3.14 \times 5 = 31.4 $ cm
- $ A = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 $ cm²
✔ C = 31.4 cm, A = 78.5 cm²
---
6. Radius = 3 cm
- $ C = 2 \times 3.14 \times 3 = 18.84 $ cm
- $ A = 3.14 \times 3^2 = 3.14 \times 9 = 28.26 $ cm²
✔ C = 18.84 cm, A = 28.26 cm²
---
7. Radius = 17 cm
- $ C = 2 \times 3.14 \times 17 = 106.76 $ cm
- $ A = 3.14 \times 17^2 = 3.14 \times 289 = 907.46 $ cm²
✔ C = 106.76 cm, A = 907.46 cm²
---
8. Radius = 18 cm
- $ C = 2 \times 3.14 \times 18 = 113.04 $ cm
- $ A = 3.14 \times 18^2 = 3.14 \times 324 = 1017.36 $ cm²
✔ C = 113.04 cm, A = 1017.36 cm²
---
9. Radius = 10 cm
- $ C = 2 \times 3.14 \times 10 = 62.8 $ cm
- $ A = 3.14 \times 10^2 = 3.14 \times 100 = 314 $ cm²
✔ C = 62.8 cm, A = 314 cm²
---
✔ Final Answers:
| # | Radius | Circumference (cm) | Area (cm²) |
|---|--------|---------------------|------------|
| 1 | 12 | 75.36 | 452.16 |
| 2 | 8 | 50.24 | 200.96 |
| 3 | 19 | 119.32 | 1133.54 |
| 4 | 9 | 56.52 | 254.34 |
| 5 | 5 | 31.4 | 78.5 |
| 6 | 3 | 18.84 | 28.26 |
| 7 | 17 | 106.76 | 907.46 |
| 8 | 18 | 113.04 | 1017.36 |
| 9 | 10 | 62.8 | 314 |
---
📝 Explanation Summary:
- We used the formulas $ C = 2\pi r $ and $ A = \pi r^2 $.
- All given values were
radii, so we didn’t need to divide by 2.
- Used $ \pi \approx 3.14 $ for simplicity (common in elementary math).
- Calculations are rounded to two decimal places where needed.
You can now fill these answers into the blank lines on the worksheet!
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of circumference worksheets.
