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Circle Formulas and Relationships

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Circle Formulas and Relationships

Circle with radius and diameter labeled

📐 Part 1: Circle Formula Knowledge

1. What is the formula for the circumference of a circle using radius?

C = πr²

C = 2πr

C = πd²

C = πr

2. What is the formula for the area of a circle?

A = 2πr

A = πd

A = πr²

A = π²r

3. If a circle has a diameter of 8 units, what is its radius?

Radius = _______ units

4. Complete the formula: C = πd is the same as C = _______

πr

2πr

πr²

π²r

🔢 Part 2: Calculate and Solve

5. Find the circumference of a circle with radius = 3 units. Leave your answer in terms of π.

Answer: C = ____________

6. Find the area of a circle with radius = 5 units. Leave your answer in terms of π.

Answer: A = ____________

7. A circular pizza has a diameter of 12 inches. What is its circumference? Use π ≈ 3.14

Answer: C ≈ ____________ inches

8. Which measurement is larger for a circle with radius 4 units: the circumference or the area? Show your work.

Circumference = ____________

Area = ____________

The ____________ is larger.

💭 Part 3: Understanding Relationships

9. Explain in your own words: What is the difference between circumference and area of a circle?
10. Look at the formulas C = 2πr and A = πr². How do you think these formulas are related? What do you notice about how radius is used in each?

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