

$$V = \frac{\pi {r}^{2} h}{3}$$
Volume
$$r = \sqrt{\frac{3 V}{\pi h}}$$
Radius
$$h = \frac{3 V}{\pi {r}^{2}}$$
Height
$$V = \frac{A_{base} h}{3}$$
Volume
By using the Pythagoras' Theorem
$$a = \sqrt{{h}^2 + {r}^2}$$
Apothem
$$h = \sqrt{{a}^2  {r}^2}$$
Height
$$r = \sqrt{{a}^2  {h}^2}$$
Radius
Lateral surface
$$S_{tot} = A_{base} + S_{lat}$$
Total surface
$$S_{lat} = S_{tot}  A_{base}$$
Lateral surface
$$S_{lat} = \pi r a$$
Lateral surface
$$r = \frac{S_{lat}}{\pi a}$$
Radius
$$r = \frac{S_{lat}}{\pi r}$$
Apothem
$$A_{base} = \pi {r}^2$$
Base area
$$A_{base} = S_{tot}  S_{lat}$$
Base area
Other formulas
$$2 r = a$$
Equilateral cone
Definition
A cone is a solid of rotation which is obtained by rotating a right triangle around one of cathetus.
Properties
 In a cone  the radius, height and apothem form a right triangle
 A cone is equivalent (has the same volume) to one third of a cylinder having the same length and radius and height as those of the cone
 An equilateral cone is a cone in which the diameter and the apothem have the same length
Cone Formulas
Data  Formula 

Volume  V = (π r^{2} h) / 3 
Radius  V = √[ (3V) / (π h) ] 
Height  h = (3V) / (π r^{2}) 
Volume  V = (A_{base} × h) / 3 
Apothem  a = √(h^{2} + r^{2}) 
Height  h = √(a^{2}  r^{2}) 
Radius  r = √(a^{2}  h^{2}) 
Total surface  S_{tot} = A_{base} + S_{lat} 
Lateral surface  S_{lat} = S_{tot}  A_{base} 
Lateral surface  S_{lat} = π r a 
Radius  r = S_{lat} / (π a) 
Apothem  a = S_{lat} / (π r) 
Base area  A_{base} = π r^{2} 
Base area  A_{base} = S_{tot}  S_{lat} 