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Volume Definition

Volume is the total amount of space enclosed or occupied in a solid. Volume generally has units of length and distance cubed (such as cm3, in3, m3 km3, etc.) In the case of a simple box calculating volume is V = L x W x H (Where V = volume, L = length, W = width, and H = height respectively). Volume can also be computed for irregularly shaped and curved solids such as cylinders or cones. The volume of a surface of revolution is particularly simple to compute due to its symmetry. For a more comprehensive breakdown of formulas for various figures see the table below.

Volume Formulas

Volume formulas for various figures including lateral surface area, area of base(s), and total surface area:

Figure

Volume

Lateral Surface Area

Area of the Base(s)

Total Surface Area

Box (also called rectangular parallelepiped, right rectangular prism)

lwh

2lh + 2wh

2lw

2lw + 2lh + 2wh

Prism

Bh

Ph

2B

Ph + 2B

Pyramid

13Bh

-

B

-

Right Pyramid

13Bh

12Ps

B

B + 12Ps

Cylinder

Bh

-

2B

-

Right Cylinder

Bh

Ph

2B

Ph + 2B

Right Circular Cylinder

πR2h

2πRh

2πR2

2πRh + 2πR2

Cone

13Bh

-

B

-

Right Circular Cone

13πR2h

πRs

πR2

πRs + πR2

Volume formulas for various figures including total surface area:

Figure

Volume

Total Surface Area

Sphere

43πr3

4πr2

Regular Tetrahedron

 2 12a3

a2 3 

Cube (regular hexahedron)

a3

6a2

Regular Octahedron

 2 3a3

2a2 3 

Regular Dodecahedron

15 + 7√ 5 4a3

3a2 25 + 10√ 5  

Regular Icosahedron

5(3 + √ 5 )12a3

5a2 3 

For the aforementioned tables:

h = height of solid

s = slant height

P = perimeter or circumference of the base

l = length of solid

B = area of the base

r = radius or sphere

w = width of solid

R = radius of the base

a = length of an edge

Other Volume Unit Definitions

  • Acre Foot (ac∙ft)

  • Acre Foot US Survey (ac∙ft)

  • Acre Inch (ac∙in)

  • Attoliter (aL)

  • Barrel Wine UK (bl)

  • Barrel UK (bl)

  • Barrel Beer US (bl)

  • Barrel Dry US (bl)

  • Barrel Liquid US (bl)

  • Barrel Petroleum US (bl)

  • Billion Cubic Meter (billion m3)

  • Board Foot Measure (FBM)

  • Bucket UK (bkt)

  • Bucket US (bkt)

  • Bushel UK (bu)

  • Bushel Dry US (bu)

  • Centiliter (cL)

  • Cord Foot Timber (cd-ft)

  • Cord Firewood (cd-ft)

  • Cubic Angstrom (A3)

  • Cubic Centimeter (cm3)

  • Cubic Cubit Ancient Egypt (cubic dhirā)

  • Cubic Decimeter (dm3)

  • Cubic Dekameter (dam3)

  • Cubic Foot (ft3)

  • Cubic Hectometer (hm3)

  • Cubic Inch (in3)

  • Cubic Kilometer (km3)

  • Cubic Meter (m3)

  • Cubic Micrometer (μm3)

  • Cubic Mile (mi3)

  • Cubic Millimeter (mm3)

  • Cubic Nanometer (nm3)

  • Cubic Picometer (pm3)

  • Cubic Yard (yd3)

  • Cup Canada (c)

  • Cup Metric (c)

  • Cup US (c)

  • Decaliter (daL)

  • Deciliter (dL)

  • Dekaliter (daL)

  • Dessertspoon Metric (dsp)

  • Dram (dr)

  • Drum Petroleum Metric (drum)

  • Drum Petroleum US (drum)

  • Exaliter (EL)

  • Femtoliter (fL)

  • Fifth (fifth)

  • Gallon UK (gal)

  • Gallon Dry US (gal)

  • Gallon Liquid US (gal)

  • Gallon US (gal)

  • Gigaliter (GL)

  • Gill UK (gi)

  • Gill US (gi)

  • Gram Sugar (g)

  • Gram Water (g)

  • Half US Gallon (half-gallon-usa)

  • Hectare Meter (ha∙m)

  • Hectoliter (hL)

  • Hogshead UK (hhd)

  • Hogshead US (hhd)

  • Imperial Gallon (gil)

  • Jack Wine (jack)

  • Jigger (jigger)

  • Kiloliter (kL)

  • Kilolitro (kL)

  • Liter (L)

  • Litro (L)

  • Measure Ancient Hebrew (measure)

  • Megaliter (ML)

  • Microliter (μL)

  • Microlitro (μL)

  • Millilitro (mL)

  • Milliliter (mL)

  • Million Cubic Meter (million m3)

  • Minim UK (min)

  • Minim US (min)

  • Nanoliter (nL)

  • Ounce Liquid UK (oz)

  • Ounce Liquid US (oz)

  • Peck UK (pk)

  • Peck US (pk)

  • Petaliter (PL)

  • Picoliter (pL)

  • Pint UK (pt)

  • Pint Dry US (pt)

  • Pint Liquid US (pt)

  • Pipe UK (pipe)

  • Pipe US (pipe)

  • Pony (pony)

  • Pottle Liquid (pottle)

  • Quart Ancient Hebrew (qt)

  • Quart Germany (qt)

  • Quart UK (qt)

  • Quart Dry US (qt)

  • Quart Liquid US (qt)

  • Quarter Liquid UK (quarter)

  • Shot (shot)

  • Stere (stere)

  • Tablespoon Metric (tbsp)

  • Tablespoon UK (tbsp)

  • Tablespoon US (tbsp)

  • Teaspoon Metric (tsp)

  • Teaspoon UK (tsp)

  • Teaspoon US (tsp)

  • Teraliter (TL)

  • Thousand Cubic Meter (thousand m3)

  • Trillion Cubic Meter (trillion m3)

  • US Fluid Ounce (fl oz)

  • Yard (yd)

For more information about other unit definitions Visit Here!

For all other definitions & terms visit All Definitions

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Sources

“Volume.” From Wolfram MathWorld, mathworld.wolfram.com/Volume.html.

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