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Circle Area and Circumference

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Circle Area and Circumference

Circle with radius and diameter illustrated

📚 Part 1: Formula Knowledge

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

A = πr²

A = 2πr

A = πd

A = r²

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

C = πr²

C = 2πr

C = πr

C = r + π

3. If a circle has a radius of 5 inches, what is its diameter?

5 inches

10 inches

15 inches

25 inches

🧮 Part 2: Calculations

4. Find the area of a circle with radius = 6 feet. Use π = 3.14. Show your work.
5. Find the circumference of a circle with diameter = 14 inches. Use π = 3.14. Show your work.
6. A circular garden has a radius of 8 feet. What is the area of the garden? Use π = 3.14.
7. A bicycle wheel has a diameter of 26 inches. How far does the bicycle travel in one complete turn of the wheel? Use π = 3.14.

🎯 Part 3: Word Problems

8. A pizza has a radius of 9 inches. What is the area of the pizza? Use π = 3.14.
9. A circular swimming pool has a circumference of 62.8 feet. What is the radius of the pool? Use π = 3.14.
10. Compare: Which has a greater area - a square with sides of 10 inches or a circle with radius of 6 inches? Show your calculations and explain your answer.

Circle Area and Circumference - Answer Key

Circle formulas reference

📚 Part 1: Formula Knowledge - Answers

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

Answer: A = πr²

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

Answer: C = 2πr

3. If a circle has a radius of 5 inches, what is its diameter?

Answer: 10 inches (diameter = 2 × radius)

🧮 Part 2: Calculations - Answers

4. Find the area of a circle with radius = 6 feet.

Answer: 113.04 square feet

Work: A = πr² = 3.14 × 6² = 3.14 × 36 = 113.04 ft²

5. Find the circumference of a circle with diameter = 14 inches.

Answer: 43.96 inches

Work: C = πd = 3.14 × 14 = 43.96 inches

6. A circular garden has a radius of 8 feet. What is the area?

Answer: 200.96 square feet

Work: A = πr² = 3.14 × 8² = 3.14 × 64 = 200.96 ft²

7. A bicycle wheel has a diameter of 26 inches. How far does it travel in one turn?

Answer: 81.64 inches

Work: C = πd = 3.14 × 26 = 81.64 inches

🎯 Part 3: Word Problems - Answers

8. A pizza has a radius of 9 inches. What is the area?

Answer: 254.34 square inches

Work: A = πr² = 3.14 × 9² = 3.14 × 81 = 254.34 in²

9. A pool has a circumference of 62.8 feet. What is the radius?

Answer: 10 feet

Work: C = 2πr, so 62.8 = 2 × 3.14 × r, so 62.8 = 6.28r, so r = 10 feet

10. Compare: Square with sides of 10 inches vs. circle with radius of 6 inches.

Answer: The square has a greater area

Square area: 10² = 100 square inches

Circle area: π × 6² = 3.14 × 36 = 113.04 square inches

Correction: The circle actually has the greater area (113.04 > 100)

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