Calculating Area and Circumference of a Circle

Key Concepts

Circle Basics:

• Radius: Distance from the center to any point on the circle.
• Diameter: Twice the radius, passing through the center to connect two points on the circle.
• Formulas:
  • Diameter (d) = 2 * radius (r)*

Area and Circumference:

• Area (A): Space within the circle.
  • Formula: A = πr²
• Circumference (C): Distance around the edge of the circle.
  • Formula: C = 2πr
• π (Pi): Approximately 3.14 (often rounded in calculations)

Example Problems

Problem 1: Given the Radius

• Radius: 5 feet
• Area Calculation:
  • Exact: 25π square feet
  • Approximate: 78.5 square feet (using π ≈ 3.14)
• Circumference Calculation:
  • Exact: 10π feet
  • Approximate: 31.4 feet

Problem 2: Given the Diameter

• Diameter: 14 inches
• Finding Radius: r = 14/2 = 7 inches
• Area Calculation:
  • Exact: 49π square inches
  • Approximate: 154 square inches
• Circumference Calculation:
  • Exact: 14π inches
  • Approximate: 44.0 inches

Problem 3: Calculate Radius from Area

• Area: 28.5 square inches
• Formula: A = πr²
• Radius: Approximate r = 3.01 inches

Problem 4: Calculate Diameter from Circumference

• Circumference: 14.5 feet
• Formula: C = 2πr
• Radius: Approximate r = 2.31 feet
• Diameter: Approximate d = 4.62 feet

Problem 5: Calculate Area from Circumference

• Circumference: 18π meters
• Radius: r = 9 meters
• Area Calculation:
  • Exact: 81π square meters
  • Approximate: 254 square meters

Problem 6: Calculate Circumference from Area

• Area: 100 square yards
• Radius Calculation: Approximate r = 5.64 yards
• Circumference Calculation:
  • Approximate: 35.4 yards

Notes:

• Units for circumference are linear (e.g., feet, inches), while units for area are squared (e.g., square feet, square inches).
• Rounding is often required for practical answers using π ≈ 3.14.