Let's solve the
Area and Circumference of a Circle worksheet step by step.
We’ll use the following formulas:
-
Circumference (C) = $ 2\pi r $ or $ \pi d $
-
Area (A) = $ \pi r^2 $
Where:
- $ r $ is the radius
- $ d $ is the diameter
- $ \pi \approx 3.14 $
---
Problem 1: Diameter = 0.8 yd
- Radius $ r = \frac{0.8}{2} = 0.4 $ yd
Circumference:
$$
C = 2\pi r = 2 \times 3.14 \times 0.4 = 2.512 \text{ yd}
$$
Area:
$$
A = \pi r^2 = 3.14 \times (0.4)^2 = 3.14 \times 0.16 = 0.5024 \text{ yd}^2
$$
✔ Answer:
- Circumference:
2.512 yd
- Area:
0.5024 yd²
---
Problem 2: Diameter = 0.9 yd
- Radius $ r = \frac{0.9}{2} = 0.45 $ yd
Circumference:
$$
C = 2\pi r = 2 \times 3.14 \times 0.45 = 2.826 \text{ yd}
$$
Area:
$$
A = \pi r^2 = 3.14 \times (0.45)^2 = 3.14 \times 0.2025 = 0.63585 \text{ yd}^2
$$
✔ Answer:
- Circumference:
2.826 yd
- Area:
0.63585 yd²
---
Problem 3: Diameter = 0.4 in
- Radius $ r = \frac{0.4}{2} = 0.2 $ in
Circumference:
$$
C = 2\pi r = 2 \times 3.14 \times 0.2 = 1.256 \text{ in}
$$
Area:
$$
A = \pi r^2 = 3.14 \times (0.2)^2 = 3.14 \times 0.04 = 0.1256 \text{ in}^2
$$
✔ Answer:
- Circumference:
1.256 in
- Area:
0.1256 in²
---
Problem 4: Diameter = 0.4 in
Same as Problem 3!
✔ Answer:
- Circumference:
1.256 in
- Area:
0.1256 in²
---
Problem 5: Diameter = 1.0 in
- Radius $ r = \frac{1.0}{2} = 0.5 $ in
Circumference:
$$
C = 2\pi r = 2 \times 3.14 \times 0.5 = 3.14 \text{ in}
$$
Area:
$$
A = \pi r^2 = 3.14 \times (0.5)^2 = 3.14 \times 0.25 = 0.785 \text{ in}^2
$$
✔ Answer:
- Circumference:
3.14 in
- Area:
0.785 in²
---
Problem 6: Diameter = 0.3 in
- Radius $ r = \frac{0.3}{2} = 0.15 $ in
Circumference:
$$
C = 2\pi r = 2 \times 3.14 \times 0.15 = 0.942 \text{ in}
$$
Area:
$$
A = \pi r^2 = 3.14 \times (0.15)^2 = 3.14 \times 0.0225 = 0.07065 \text{ in}^2
$$
✔ Answer:
- Circumference:
0.942 in
- Area:
0.07065 in²
---
✔ Final Answers Summary:
| Problem | Diameter | Circumference | Area |
|--------|----------|----------------|-------|
| 1 | 0.8 yd | 2.512 yd | 0.5024 yd² |
| 2 | 0.9 yd | 2.826 yd | 0.63585 yd² |
| 3 | 0.4 in | 1.256 in | 0.1256 in² |
| 4 | 0.4 in | 1.256 in | 0.1256 in² |
| 5 | 1.0 in | 3.14 in | 0.785 in² |
| 6 | 0.3 in | 0.942 in | 0.07065 in² |
> 🔍
Note: You can round answers to two decimal places if needed (e.g., 0.50 yd², 2.51 yd), but exact values are shown here for accuracy.
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of circle area and perimeter worksheet.
