Cone
Cone
A 3D shape bounded by a base and a vertex connected by a curved surface.
Properties
  1. Apex: The vertex of the cone.
  2. Height (h): The perpendicular distance between the base and the apex.
  3. Slant Height (l): The length of a line segment connecting the circumference of the base and the apex.
  4. Radius: Radius of the base is the radius of the cone.
  5. Axis: The line segment connecting the center of the base and the apex.
  6. Directrix: The perimeter of the base of the cone.
  7. Generatrix: A line segment connecting the directrix and the apex.
  8. Aperture: The maximum angle possible between two generatrix lines.
Types of Cones
  1. Right Cone: Axis is perpendicular to the base.
  2. Oblique Cone: Axis is not perpendicular to the base.
  3. Circular Cone: Base is circular in shape.
  4. Elliptical Cone: Base is elliptical in shape.
  5. Right-Circular Cone: Axis is perpendicular to the circular base.
Facts
  1. The term “cone” is derived from the Greek word konos, which means a wedge or a peak.
Volume of Right-Circular Cone (V)
V =
1 3
π r2 h
r: radius, h: height
Total Surface Area of Right-Circular Cone (TSA)
TSA = π r (l + r)
r: radius, l: slant height
Lateral Surface Area of Right-Circular Cone (LSA)
LSA = π r l
r: radius, l: slant height
Slant Height of Right-Circular Cone (l)
l = r2 + h2
r: radius, h: height