Lecture on Circular Shapes: Area, Perimeter, and Volume

Basic Terminology

• Radius: Distance from the center of a circle to the edge.
  • Constant regardless of the point on the circle.
• Diameter: Distance across the span of the circle.
  • Equals twice the radius.
• Circumference: Distance around the outside of the circle (perimeter).
• Pi (π): Greek letter representing the constant approximate value of 3.14 used in circle calculations.

Calculating Area of a Circle

• Formula: Area = π * R²
• Example 1:
  • Radius = 5 cm
  • Area = 3.14 * 5 * 5 = 78 cm²
• Example 2:
  • Radius = 11 m
  • Area = 3.14 * 11 * 11 = 380.13 m²
• Process: Substitute radius into the formula π * R².

Calculating Circumference of a Circle

• Formula: Circumference = 2 * π * R
• Example 1:
  • Radius = 9 cm
  • Circumference = 2 * 3.14 * 9 = 56.55 cm
• Example 2:
  • Diameter = 9 cm
  • Radius = Diameter / 2 = 4.5 cm
  • Circumference = 2 * 3.14 * 4.5 = 28.2 cm

Calculating Volume of a Cylinder

• Volume Formula: Volume = Area of circle * Height
  • Where Area of circle = π * R²
• Example 1:
  • Radius = 4 cm, Height = 11 cm
  • Volume = 3.14 * 4 * 4 * 11 = 552.96 cm³
• Example 2:
  • Diameter = 12 m, Height = 7 m
  • Radius = Diameter / 2 = 6 m
  • Volume = 3.14 * 6 * 6 * 17 = 1922.65 m³

Summary of Formulas

• Area of a Circle: π * R²
• Circumference of a Circle: 2 * π * R
• Volume of a Cylinder: π * R² * Height*

Note: Understanding these formulas and how to substitute the given values will help in solving problems related to circular shapes.