Cylinder Calculator 3D

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Cylinder graphic:

Cylinder graphic 3d

Results:

Insert two values for the cylinder:

Use keys and for value changes

r h d = 2·r p = 2·π·r AB = π·r2 AL = 2·π·r·h AS = 2·π·r·(r+h) V = π·r2·h

Precision with 3 decimal places

Interactive 3D-Cylinder

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All formulas for the Cylinder at a glance

Here you see the necessary formulas for the calculation of a right circular cylinder:

cylinder formulas

Link to graphic: https://www.matheretter.de/img/cylinder/formulas.png

Explanations:

Diameter = 2·radius → d = 2·r

Perimeter = 2·Pi·radius → p = 2·π·r

Base Area = Pi·radius² → AB = π·r²

Lateral Surface = perimeter · height → AL = 2·π·r·h

Surface Area = 2·base area + lateral surface → AS = 2·π·r² + 2·π·r·h = 2·π·r·(r+h)

Volume = base area · height → V = π·r²·h

What is a cylinder?

Definition: A cylinder (circular cylinder) consists of two parallel opposite circular areas and one rectangular lateral surface, that is perpendicular to the circular areas (base area and top surface). A cylinder is a geometrical shape. Circles are of fundamental importance for this shape, therefore we need the formulas for the circle (circular area and perimeter of a circle).
For the circular cylinder there are the following formulas: The perimeter p is 2·Pi·r (this is the formula for the perimeter of the circle), the base area AB is Pi·r² (this is the formula for the area of a circle), the lateral surface is perimeter times height, AL = p·h and therefore AL = 2·Pi·r·h, the surface area consists of the circular areas on top and on bottom (2 times the base area) and the lateral surface, so surface is AS = 2·AB + AL and thus AS = 2·(π·r²) + (2·π·r·h), while the 2·π·r is often factored out and we get: AS = 2·π·r·(r+h). The volume of the cylinder is base area times height, thus V = AB·h = π·r²·h. cylinder with radius, base area and diameter of the base area. Characteristics of a cylinder.

Example from daily life (form of a cylinder):
Drinking glass, pipe, building stone, engine cylinder, chair leg, pen, form of a pill etc.

Flächenberechnung beim Zylinder (Grafik):

Area calculation of the cylinder: lateral surface, base area, top surface und total surface
Possible combinations and calculations for given cylinder values
Value 1 Value 2 Radius
computable
Height
computable
Solution formula for radius
Radius is always computable
Solution formula for height
Radius is partially assumed
Radius Height yes yes Radius provided Height provided
Radius Perimeter yes no Radius provided Height not computable - Details
Radius Base area yes no Radius provided Height not computable - Details
Radius Surface area yes yes Radius provided h = AS / 2·π·r – r
See equivalent transformation
Radius Lateral surface yes yes Radius provided h = AL/2·π·r
See equivalent transformation
Radius Volume yes yes Radius provided h = V/r2·h
See equivalent transformation
Height Perimeter yes yes r = p / 2·π
See equivalent transformation
Height provided
Height Base area yes yes r = AB/π
See equivalent transformation
Height provided
Height Surface area yes yes r1,2 = – h/2 ± √( h2/4 + AS/2·π )
See equivalent transformation
Height provided
Height Lateral surface yes yes r = AL/2·π·h
See equivalent transformation
Height provided
Height Volume yes yes r = ± √( V/h·π )
See equivalent transformation
Height provided
Perimeter Base area yes no r = p / 2·π
See equivalent transformation
Height not computable - Details
Perimeter Surface area yes yes r = p / 2·π
See equivalent transformation
h = AS / p – r
See equivalent transformation
Perimeter Lateral surface yes yes r = p / 2·π
See equivalent transformation
h = AL / p
See equivalent transformation
Perimeter Volume yes yes r = p / 2·π
See equivalent transformation
h = 2·V / u·r
See equivalent transformation
Base area Surface area yes yes r = AB/π
See equivalent transformation
h = r · AS / 2·AB – r
See equivalent transformation
Base area Lateral surface yes yes r = AB/π
See equivalent transformation
h = r · AL / 2·AB
See equivalent transformation
Base area Volume yes yes r = AB/π
See equivalent transformation
h = AL / AB
See equivalent transformation
Surface area Lateral surface yes yes If we have the height, we can calculate
the radius from the formule of the lateral surface:

r = AL / 2·π·h
See equivalent transformation
h = ± √( AL2 / 2·π·AS – 2·π·M )
See equivalent transformation
Surface area Volume yes yes 0 = r3 + AS / -2·π · r + V / π
3 Solutions for the cubic equation
See equivalent transformation
If we have the height, we can calculate
the radius from the formule of the lateral surface:

h = AS / 2·π·r – r
See equivalent transformation
Lateral surface Volume yes yes r = 2·V/AL
See equivalent transformation
If we have the height, we can calculate
the radius from the formule of the lateral surface:

h = AL/2·π·r
See equivalent transformation
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