Area and Circumference of a Circle

Radius and Diameter

  • Radius: Distance from the center to any point on the circle.

  • Diameter: Distance across the circle through the center; twice the radius (d=2rd = 2r).

Area of a Circle

  • The area is calculated by: Area=πr2\text{Area} = \pi r^2

  • Where: π≈3.14159\pi \approx 3.14159 (commonly approximated as 3.14)

Circumference of a Circle

  • The circumference is calculated by: Circumference=2πr\text{Circumference} = 2 \pi r

  • If you walk around the circle you would travel 31.4 feet.

Example Calculation

  • Given radius r=5 feetr = 5 \text{ feet}, using π=3.14\pi = 3.14

    • Area: Area=3.14×(5 ft)2=3.14×25 ft2=78.5 ft2\text{Area} = 3.14 \times (5 \text{ ft})^2 = 3.14 \times 25 \text{ ft}^2 = 78.5 \text{ ft}^2

    • Circumference: Circumference=2×3.14×5 ft=10×3.14 ft=31.4 ft\text{Circumference} = 2 \times 3.14 \times 5 \text{ ft} = 10 \times 3.14 \text{ ft} = 31.4 \text{ ft}