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

$$\displaystyle V=\frac{A·h}{3}$$

$$\displaystyle V=\frac{r^2· h}{3}$$