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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 Practice

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 = 2r²

3. If the radius of a circle is 5 inches, what is the 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

Area = __________ square feet

5. Find the circumference of a circle with radius = 4 inches. Use π = 3.14

Circumference = __________ inches

6. A circular garden has a diameter of 12 feet. What is its area? Use π = 3.14

Area = __________ square feet

7. A bicycle wheel has a radius of 14 inches. How far does the bicycle travel in one complete rotation of the wheel? Use π = 3.14

Distance = __________ inches

🎯 Part 3: Word Problems

8. A pizza has a diameter of 16 inches. What is the area of the pizza? Use π = 3.14

Pizza area = __________ square inches

9. A circular pond has a circumference of 31.4 meters. What is the radius of the pond? Use π = 3.14

Radius = __________ meters

10. Compare: Which has a larger area - a square with sides of 8 feet or a circle with radius of 5 feet? Show your work. Use π = 3.14

Circle Area and Circumference - ANSWER KEY

📐 Part 1: Formula Practice - 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 the radius of a circle is 5 inches, what is the diameter?

Answer: 10 inches (diameter = 2 × radius)

🔢 Part 2: Calculations - ANSWERS

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

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

Answer: 113.04 square feet

5. Find the circumference of a circle with radius = 4 inches.

Work: C = 2πr = 2 × 3.14 × 4 = 25.12

Answer: 25.12 inches

6. A circular garden has a diameter of 12 feet. What is its area?

Work: radius = 12 ÷ 2 = 6 feet; A = πr² = 3.14 × 6² = 3.14 × 36 = 113.04

Answer: 113.04 square feet

7. A bicycle wheel has a radius of 14 inches. How far does the bicycle travel in one complete rotation?

Work: C = 2πr = 2 × 3.14 × 14 = 87.92

Answer: 87.92 inches

🎯 Part 3: Word Problems - ANSWERS

8. A pizza has a diameter of 16 inches. What is the area?

Work: radius = 16 ÷ 2 = 8 inches; A = πr² = 3.14 × 8² = 3.14 × 64 = 200.96

Answer: 200.96 square inches

9. A circular pond has a circumference of 31.4 meters. What is the radius?

Work: C = 2πr, so 31.4 = 2 × 3.14 × r; 31.4 = 6.28r; r = 31.4 ÷ 6.28 = 5

Answer: 5 meters

10. Compare: Which has a larger area - a square with sides of 8 feet or a circle with radius of 5 feet?

Work: Square area = 8² = 64 square feet; Circle area = 3.14 × 5² = 3.14 × 25 = 78.5 square feet

Answer: The circle has a larger area (78.5 > 64)

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