

$$V = \pi r^2 \times h$$
Volume
$$r = \sqrt{\frac{V}{\pi h}}$$
Radius
$$h = \frac{V}{\pi {r}^2}$$
Radius
$$V = A_{base} \times h$$
Volume
$$A_{base} = \frac{V}{h}$$
Base area
$$h = \frac{V}{A_{base}}$$
Height
$$S_{lat} = 2 \pi r \times h$$
Lateral surface
$$r = \frac{V}{2 \pi h}$$
Radius
$$h = \frac{V}{2 \pi r}$$
Height
$$A_{base} =\pi {r}^2$$
Base area (Area of the circle)
$$r = \sqrt{\frac{A_{base}}{\pi}}$$
Radius
$$S_{tot} = 2 \times A_{base} + S_{lat}$$
Total surface
$$S_{lat} = S_{tot}  2 \times A_{base}$$
Lateral surface
$$A_{base} = \frac{S_{tot}  S_{lat}}{2}$$
Base area
Equilateral Cylinder
$$2r = h$$
Diameter
Definition
The cylinder is a solid obtained by the complete rotation of a rectangle around one of its sides.
Properties
 In the rectangle that generates the cylinder, the side around which the rotation occurs is the height of the cylinder, while the other side is the radius.
 The height of the cylinder is generally represented by a segment that joins the centers of the two bases, more generally the height of the cylinder is any perpendicular segment that joins the two bases.
Other definitions
 An equilateral cylinder is a cylinder in which the base diameter and height are congruent.
Cylinder Formulas
Data  Formula 

Volume  V = π r × h 
Radius  r = √( V / (π × h) ) 
Height  h = V / (π × r^{2}) 
Volume  V = A_{base} × h 
Base area  A_{base} = V / h 
Height  h = V / A_{base} 
Lateral surface  S_{lat} = 2 π r × h 
Radius  r = V / (2 π h) 
Height  h = V / (2 π r) 
Base area  A_{base} = π r^{2} 
Radius  r = √( A_{base} / π ) 
Total surface  S_{tot} = 2 × A_{base} + S_{lat} 
Lateral surface  S_{lat} = S_{tot}  2 × A_{base} 
Base area  A_{base} = (S_{tot}  S_{lat}) / 2 
Equilateral Cylinder Formulas
Data  Formula 

Diameter  2r = h 