## Volume — Wikipedia

Volume | |
---|---|

Common symbols | V |

SI unit | Cubic metre [m^{3}] |

Other units | Litre, Fluid ounce, gallon, quart, pint, tsp, fluid dram, in^{3}, yd^{3}, barrel |

In SI base units | 1 m^{3} |

Dimension | L^{3} |

**Volume** is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.^{[1]} Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.

Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape’s boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.

The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.^{[2]}

In *differential geometry*, volume is expressed by means of the

en.wikipedia.org

## Area and Volume Formula for geometrical figures

pi (π)=3.1415926535 …

## Perimeter formula | |

Square | 4 × side |

Rectangle | 2 × (length + width) |

Parallelogram | 2 × (side1 + side2) |

Triangle | side1 + side2 + side3 |

Regular n-polygon | n × side |

Trapezoid | height × (base1 + base2) / 2 |

Trapezoid | base1 + base2 + height × [csc(theta1) + csc(theta2)] |

Circle | 2 × pi × radius |

Ellipse | 4 × radius1 × E(k,pi/2) E(k,pi/2) is the Complete Elliptic Integral of the Second Kind k = (1/radius1) × sqrt(radius1 ^{2} — radius2^{2}) |

## Area formula | |

Square | side^{2} |

Rectangle | length × width |

Parallelogram | base × height |

Triangle | base × height / 2 |

Regular n-polygon | (1/4) × n × side^{2} × cot(pi/n) |

Trapezoid | height × (base1 + base2) / 2 |

Circle | pi × radius^{2} |

Ellipse | pi × radius1 × radius2 |

Cube (surface) | 6 × side^{2} |

Sphere (surface) | 4 × pi × radius^{2} |

Cylinder (surface of side) | perimeter of circle × height |

2 × pi × radius × height | |

Cylinder (whole surface) | Areas of top and bottom circles + Area of the side |

2(pi × radius^{2}) + 2 × pi × radius × height | |

Cone (surface) | pi × radius × side |

Torus (surface) | pi^{2} × (radius2^{2} — radius1^{2}) |

## Volume formula | |

Cube | side^{3} |

Rectangular Prism | side1 × side2 × side3 |

Sphere | (4/3) × pi × radius^{3} |

Ellipsoid | (4/3) × pi × radius1 × radius2 × radius3 |

Cylinder | pi × radius^{2} × height |

Cone | (1/3) × pi × radius^{2} × height |

Pyramid | (1/3) × (base area) × height |

Torus | (1/4) × pi^{2} × (r1 + r2) × (r1 — r2)^{2} |

Source: Spiegel, Murray R. Mathematical Handbook of Formulas and Tables.

Schaum’s Outline series in Mathematics. McGraw-Hill Book Co., 1968.

www.science.co.il

## Cylinder Volume & Surface Area Calculator

** cylinder calculator** — step by step calculation, formulas & solved example problem to find the volume & the base, total & lateral surface area of a cylinder for the given base radius & height value in different measurement units between inches (in), feet (ft), meters (m), centimeters (cm) & millimeters (mm). In geometry, cylinder is a solid or hollow figure with round ends and long straight sides. The cylinder formulas, solved example & step by step calculations may useful for users to understand how the input values are being used in such calculations. Also this featured cylinder calculator uses the various conversion functions to find its area, volume & slant height in SI or metric or US customary units.

__Cylinder & its Formulas__

The following mathematical formulas are used in this cylinder calculator to find the volume & the base, total & lateral surface area of a cylinder for the given base radius & height values.

__Solved Example__

The below solved example problem may be useful to understand how the values are being used in the mathematical formulas to find the volume & the base, total & lateral surface area of a cylinder for the given base radius & height values.

**Example Problem :**

Find the volume & the base, total & lateral surface area of a cylinder having the base radius & height of 18 cm & 27 cm respectively?

**Solution :**

The given values

base radius r = 18 cm

height h = 27 cm

**Step by step calculation**

formula to find volume = π r^{2} h

substitute the values

= π x 18^{2} x 27

= **27493.71 cm ^{3}**

formula to find total surface area = 2 π r (h + r)

substitute the values

= 2 x π x 18 x (27 + 18)

=

**5091.42 cm**

^{2}formula to find base surface area = π r

^{2}

substitute the values

= π x 18

^{2}x 27

=

**1018.28 cm**

^{2}formula to find lateral surface area = 2 π r h

substitute the values

= 2 x π x 18 x 27

=

**3054.85 cm**

^{2}

The volume & the base, total & lateral surface area of a cylinder may required to be calculated in SI or metric or US customary unit systems, therefore this cylinder calculator is featured with major measurement units conversion function to find the output values in different customary units such as inches (in), feet (ft), meters (m), centimeters (cm) & millimeters (mm) by using this below conversion table.

10 mm = 1 cm100 mm = 3.93 in1000 mm = 3.28 ft1000 mm = 1 m | 1 cm = 10 mm10 cm = 3.93 in100 cm = 3.28 ft100 cm = 1 m | 1 ft = 3048 mm1 ft = 304.8 cm1 ft = 12 in10 ft = 3.048 m | 1 in = 25.4 mm1 in = 2.54 cm100 in = 8.33 ft100 in = 2.54 m |

In the field of *area & volume calculations*, finding the volume & surface area of cylinder is very important to understand the element of basic mathematics. The above formulas, step by step calculation & solved example may helpful for users to understand the how to calculate the volume & surface area of cylinder manually, however, when it comes to online to perform quick calculations, this cylinder calculator may be useful to find the results.

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## Volume formulas

Here, we provide you with volume formulas for some common three-dimensional figure.

**Cube:**

Volume = a^{3} = a × a × a

**Cylinder:**

Volume = pi × r^{2} × h

pi = 3.14

h is the height

r is the radius

**Rectangular solid:**

Volume = l × w × h

l is the length

w is the width

h is the height

**Sphere:**

Volume = (4 × pi × r^{3})/3

pi = 3.14

r is the radius

**Cone:**

Volume = (pi × r^{2} × h)/3

pi = 3.14

r is the radius

h is the height

**Pyramid:**

Volume = (B × h)/3

B is the area of the base

h is the height

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