Circle Calculations

Key Concepts

• Circle Components
  • Center: Point in the middle of the circle.
  • Radius (R): Distance from the center to any point on the circle.
  • Diameter (D): Distance across the circle through the center; D = 2R.

Formulas

1. Area of a Circle:

   • Formula: A = πr²
   • Where π (Pi) ≈ 3.14 (exact value is 3.141592654...)

2. Circumference of a Circle:

   • Formula: C = 2πr
   • Distance around the edge of the circle.

Example Problems

Problem 1: Radius = 5 feet

• Area Calculation:

  • A = π(5)² = 25π square feet
  • Approximation: A ≈ 25 × 3.14 = 78.5 square feet

• Circumference Calculation:

  • C = 2π(5) = 10π feet
  • Approximation: C ≈ 10 × 3.14 = 31.4 feet

Problem 2: Diameter = 14 inches

• Calculate the radius: R = D/2 = 14/2 = 7 inches

• Area Calculation:

  • A = π(7)² = 49π square inches
  • Approximation: A ≈ 49 × 3.14 = 154 square inches

• Circumference Calculation:

  • C = 2π(7) = 14π inches
  • Approximation: C ≈ 14 × 3.14 = 44.0 inches

Problem 3: Area = 28.5 square inches

• Finding Radius:
  • A = πr²
  • 28.5 = 3.14r²
  • r² = 28.5 / 3.14 ≈ 9.08
  • r = √9.08 ≈ 3.01 inches

Problem 4: Circumference = 14.5 feet

• Finding Diameter:
  • C = 2πr
  • 14.5 = 2πr
  • r = 14.5 / (2 × 3.14) ≈ 2.31 feet
  • D = 2r = 4.62 feet

Problem 5: Circumference = 18π meters

• Finding Area:
  • C = 2πr
  • 18π = 2πr
  • r = 18 / 2 = 9 meters
  • Area: A = π(9)² = 81π square meters
  • Approximation: A ≈ 81 × 3.14 = 254 square meters

Problem 6: Area = 100 square yards

• Finding Circumference:
  • A = πr²
  • 100 = 3.14r²
  • r² = 100 / 3.14 ≈ 31.85
  • r = √31.85 ≈ 5.64 yards
  • C = 2πr ≈ 2 × 3.14 × 5.64 ≈ 35.4 yards

Summary

• Area is expressed in square units (e.g., square feet, square yards).
• Circumference is expressed in linear units (e.g., feet, yards).
• Remember to match units for radius, diameter, and circumference, while area will always be in square units.