Geometry - Cone

Cone

Definition, Properties, and Formulae of a Cone

A cone is a three-dimensional geometric shape with a circular base and a single apex. The cone can be defined by the following parameters:

  • Radius (r): The radius of the circular base of the cone.
  • Height (h): The vertical distance from the apex to the center of the base.
  • Slant Height (s): The distance from the apex to any point on the circumference of the base.

Cone

Key Parameters

  • \( r \): Radius of the cone's base
  • \( h \): Height of the cone
  • \( s \): Slant height of the cone (calculated using Pythagoras theorem: \( s = \sqrt{h^2 + r^2} \))

1. Volume of the Cone \(V\)

\[ V = \frac{1}{3} \pi h (R^2 + r^2 + Rr) \]

This formula calculates the volume of a cone, which is the amount of space inside it. The formula takes into account both the radius

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