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Circle Area Circumference Problems

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Circle Area Circumference Problems

Circle with radius and circumference labeled

📐 Part 1: Circumference Word Problems

Remember: Circumference = 2πr or πd (Use π ≈ 3.14)

1. A bicycle wheel has a radius of 14 inches. What is the circumference of the wheel? Round to the nearest inch.

Answer: __________ inches

2. Sarah is building a circular garden with a diameter of 12 feet. How much fencing will she need to go around the entire garden?

Answer: __________ feet

3. A pizza has a radius of 8 inches. What is the distance around the edge of the pizza (circumference)?

Answer: __________ inches

4. A circular track has a circumference of 628 feet. What is the radius of the track? (Hint: solve for r)

Answer: __________ feet

⭕ Part 2: Area Word Problems

Remember: Area = πr² (Use π ≈ 3.14)

5. A circular swimming pool has a radius of 10 feet. What is the area of the pool's surface?

Answer: __________ square feet

6. A circular rug has a diameter of 6 feet. What is the area of the rug?

Answer: __________ square feet

7. Jake wants to plant grass in a circular area with a radius of 15 feet. If grass seed costs $2 per square foot, how much will it cost to cover the entire area?

Area: __________ square feet

Total Cost: $ __________

8. A circular tablecloth covers a table with an area of 113.04 square inches. What is the radius of the tablecloth?

Answer: __________ inches

🔄 Part 3: Mixed Practice

9. A circular fountain has a radius of 7 feet. Find both the circumference and the area.

Circumference: __________ feet

Area: __________ square feet

10. Maria is designing a circular logo. She wants the area to be approximately 78.5 square inches. What should the radius be?

Answer: __________ inches

Circle Area Circumference Problems - Answer Key

Circle formulas diagram

📐 Part 1: Circumference Answers

1. Bicycle wheel (r = 14 inches)

Work: C = 2πr = 2 × 3.14 × 14 = 87.92 inches

Answer: 88 inches

2. Circular garden (d = 12 feet)

Work: C = πd = 3.14 × 12 = 37.68 feet

Answer: 37.68 feet

3. Pizza (r = 8 inches)

Work: C = 2πr = 2 × 3.14 × 8 = 50.24 inches

Answer: 50.24 inches

4. Track (C = 628 feet)

Work: 628 = 2πr → r = 628 ÷ (2 × 3.14) = 628 ÷ 6.28 = 100 feet

Answer: 100 feet

⭕ Part 2: Area Answers

5. Swimming pool (r = 10 feet)

Work: A = πr² = 3.14 × 10² = 3.14 × 100 = 314 square feet

Answer: 314 square feet

6. Circular rug (d = 6 feet, r = 3 feet)

Work: A = πr² = 3.14 × 3² = 3.14 × 9 = 28.26 square feet

Answer: 28.26 square feet

7. Grass area (r = 15 feet)

Work: A = πr² = 3.14 × 15² = 3.14 × 225 = 706.5 square feet

Cost = 706.5 × $2 = $1,413

Area: 706.5 square feet

Total Cost: $1,413

8. Tablecloth (A = 113.04 square inches)

Work: 113.04 = πr² → r² = 113.04 ÷ 3.14 = 36 → r = 6 inches

Answer: 6 inches

🔄 Part 3: Mixed Practice Answers

9. Fountain (r = 7 feet)

Circumference: C = 2πr = 2 × 3.14 × 7 = 43.96 feet

Area: A = πr² = 3.14 × 7² = 3.14 × 49 = 153.86 square feet

10. Logo design (A = 78.5 square inches)

Work: 78.5 = πr² → r² = 78.5 ÷ 3.14 = 25 → r = 5 inches

Answer: 5 inches

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