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Volume

Volume

The total amount of space enclosed in a solid.

For the following 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 of sphere
w = width of solid R = radius of the base a = length of an edge

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 Formula: one-third times B times h - B -
Right Pyramid Formula: one-third times B times h Formula: one-half times P times s B B + (1/2)Ps, formula for total surface area of a right regular pyramid, where B is base area, P is perimeter, s is slant height.
Cylinder Bh - 2B -
Right Cylinder Bh Ph 2B Ph + 2B
Right Circular Cylinder πR2h 2πRh 2πR2 2πRh + 2πR2
Cone Formula: one-third times B times h - B -
Right Circular Cone Formula: (1/3)πR²h πRs or Formula: pi times R times the square root of (R squared plus h squared) πR2 πRs + πR2 or Formula: πR√(R² + h²) + πR²

Figure Volume Total Surface Area
Sphere Formula: (4/3)πr³ Formula: 4πr²
Regular Tetrahedron The formula: (√2 / 12) a³ Mathematical expression: a squared times square root of 3
Cube (regular hexahedron) a3 6a2
Regular Octahedron Formula for the volume of a regular octahedron: (√2/3)a³, where a is the edge length. The formula: 2a²√3
Regular Dodecahedron Surface area formula for a regular dodecahedron: (15 + 7√5) / 4 × a³, where a is edge length. Surface area formula: 3a² times the square root of (25 + 10√5), where a is edge length.
Regular Icosahedron Volume formula for a regular icosahedron: V = 5(3 + √5)/12 × a³, where a is edge length 5a²√3

For the tables above,
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 of sphere
w = width of solid R = radius of the base a = length of an edge

 

See also

Lateral surface, right prism, right regular pyramid, frustum of a cone or pyramid, torus, solid of revolution, volume by parallel cross-sections