Subjects geometry

Circle Area Circumference 7A487A

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. Problem: Find the area of circles given the circumference. 2. Formula: Circumference $C = 2\pi r$ and Area $A = \pi r^2$. 3. Important: Use $\pi = 3.14$ and solve for radius $r$ first by rearranging circumference formula: $$r = \frac{C}{2\pi}$$ 4. Number 20: $C = 6\pi$ ft Calculate radius: $$r = \frac{6\pi}{2\pi} = \frac{6\cancel{\pi}}{2\cancel{\pi}} = 3 \text{ ft}$$ Calculate area: $$A = 3.14 \times 3^2 = 3.14 \times 9 = 28.26 \text{ ft}^2$$ 5. Number 22: $C = 24\pi$ cm Calculate radius: $$r = \frac{24\pi}{2\pi} = \frac{24\cancel{\pi}}{2\cancel{\pi}} = 12 \text{ cm}$$ Calculate area: $$A = 3.14 \times 12^2 = 3.14 \times 144 = 452.16 \text{ cm}^2$$ 6. Number 23: $d = 30$ m Radius: $$r = \frac{d}{2} = \frac{30}{2} = 15 \text{ m}$$ Calculate circumference: $$C = 2 \times 3.14 \times 15 = 94.2 \text{ m}$$ Calculate area: $$A = 3.14 \times 15^2 = 3.14 \times 225 = 706.5 \text{ m}^2$$ 7. Number 25: $r = 3.1$ cm Calculate circumference: $$C = 2 \times 3.14 \times 3.1 = 19.468 \text{ cm}$$ Calculate area: $$A = 3.14 \times 3.1^2 = 3.14 \times 9.61 = 30.1594 \text{ cm}^2$$ Final answers: 20. Area = 28.26 ft^2 22. Area = 452.16 cm^2 23. Circumference = 94.2 m, Area = 706.5 m^2 25. Circumference = 19.468 cm, Area = 30.1594 cm^2