Circle Calculations Overview

Overview

This lecture explains how to calculate the area and circumference of a circle, including definitions, formulas, and example problems using radius and diameter.

Circle Basics

• The center of a circle is the point exactly in the middle.
• The radius (r) is the distance from the center to any point on the circle.
• The diameter (d) is twice the radius: d = 2r.

Area and Circumference Formulas

• The area (A) of a circle is given by: A = πr².
• The circumference (C) of a circle is given by: C = 2πr.
• π (pi) is approximately 3.14 for calculations.

Example 1: Given Radius

• For a circle with radius 5 ft:
  • Area = π × 5² = 25π ≈ 78.5 square feet.
  • Circumference = 2π × 5 = 10π ≈ 31.4 feet.

Example 2: Given Diameter

• For a circle with diameter 14 in:
  • Radius = 14 ÷ 2 = 7 in.
  • Area = π × 7² = 49π ≈ 154 square inches.
  • Circumference = 2π × 7 = 14π ≈ 44.0 inches (rounded).

Finding Radius from Area

• Given area = 28.5 square inches:
  • Use formula: Area = πr².
  • 28.5/3.14 ≈ 9.08; then √9.08 ≈ 3.01 inches (radius, rounded).

Finding Diameter from Circumference

• Given circumference = 14.5 feet:
  • Use formula: C = 2πr.
  • 14.5/6.28 ≈ 2.31 feet (radius, rounded).
  • Diameter = 2 × 2.31 ≈ 4.62 feet.

Finding Area from Circumference (with π)

• Given circumference = 18π meters:
  • Radius = 18π / 2π = 9 meters.
  • Area = π × 9² = 81π ≈ 254 square meters.

Finding Circumference from Area

• Given area = 100 square yards:
  • 100/3.14 ≈ 31.85; then √31.85 ≈ 5.64 yards (radius, rounded).
  • Circumference = 2π × 5.64 ≈ 35.4 yards.

Key Terms & Definitions

• Radius (r) — distance from center to circle's edge.
• Diameter (d) — straight line passing through center, connecting two points on circle; d = 2r.
• Circumference (C) — distance around the circle's edge; C = 2πr.
• Area (A) — measure of space inside circle; A = πr².
• Pi (π) — mathematical constant ≈ 3.14.

Action Items / Next Steps

• Practice solving circle problems using different given values (radius, diameter, area, or circumference).
• Use π = 3.14 unless stated otherwise.
• Ensure units are consistent and area is always in square units.