Cone calculation

Description and formulas for the calculation of Cones

Cone Definition

  • A cone is a solid with a circular base and one vertex

  • Cones have two faces (the base and the curved surface), one edge that connects the base to the curved surface, and one vertex (called the apex)

  • If the apex over the center of the base surface, we call it right cone. If the apex deviates from the center of the base surface, this is called a oblique cone

Formelas for caltulation of cones

The following formulas refer to the calculation of a apex cone

Calculate base radius \(r\) of a cone

\(\displaystyle r=\sqrt{\frac{A}{ π}}\)

Calculate base diameter \(d\) of a cone

\(\displaystyle d=\sqrt{\frac{4·A}{π}}\)

\(\displaystyle d=2· r\)

Calculate height \(h\) of a cone

\(\displaystyle h=\sqrt{L^2-r^2}\)

\(\displaystyle h=\frac{3·V}{A}\)

Calculate slant height \(L\) of a cone

\(\displaystyle L=\sqrt{h^2+r^2}\)

Calculate lateral surface \(S_I\) of a cone

\(\displaystyle S_I=\frac{d·π·L}{2}\)

\(\displaystyle S_I=\frac{P· L}{2}\)

Calculate surface \(S\) of a cone

\(\displaystyle S=S_I+A\)

Calculate volume \(V\) of a cone

\(\displaystyle V=\frac{A·h}{3}\)

\(\displaystyle V=\frac{r^2· h}{3}\)