Circle Measurements
1. The problem requires us to complete the table by finding missing diameters and areas of circles given some radius and diameter values. We use the formulas:
- Diameter $d = 2r$ where $r$ is the radius.
- Area $A = \pi r^2$ with $\pi = 3.14$.
2. Given radius 12 m (row 1):
- Diameter $= 2 \times 12 = 24$ m.
- Area $= 3.14 \times 12^2 = 3.14 \times 144 = 451.84$ m² (not asked but just for clarity).
3. For diameter 16 in (row 2):
- Radius $r = \frac{16}{2} = 8$ in.
- Area $= 3.14 \times 8^2 = 3.14 \times 64 = 200.96$ in².
4. For area $153.86$ cm² (row 4):
- Use $A = 3.14 r^2$ to find radius:
$$r^2 = \frac{153.86}{3.14} = 49$$
$$r = \sqrt{49} = 7 \text{ cm}$$
- Diameter $= 2 \times 7 = 14$ cm.
5. For diameter missing in row 3 with radius 12 m (already done): diameter is 24 m.
6. For area missing in row 5 with radius 12 m (already done step 2): area is $451.84$ m².
Summary of missing values:
- Row 1 diameter: 24 m
- Row 2 area: 200.96 in²
- Row 3 diameter: 24 m (same as row 1 radius)
- Row 4 radius: 7 cm, diameter: 14 cm
- Row 5 area: 451.84 m²
Final answers:
| Radius | Diameter | Area |
|--------|----------|------------|
| 12 m | 24 m | 451.84 m² |
| 8 in | 16 in | 200.96 in² |
| 7 cm | 14 cm | 153.86 cm² |