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Volume Formulas for Geometric Shapes.

Volume
is the amount of space that an object occupies; measured in units cubed.

Volume of a Cube

Cube

The volume of a Cube is equal to the cube of the length of its edge.

Volume formula of a Cube:

V = a3

where V - a cube volume,
a - the length of an edge.

Volume of a Prism

Prism

The volume of a prism is equal to the product of the base area to a height of a prism.

Volume formula of a prism:


V = Ab · h

where V - volume of the prism,
Ab - the area of the base of the prism,
h - the height of the prism.

Volume of a parallelepiped

parallelepiped

The volume of a parallelepiped is equal to the product of the base area to a height of a parallelepiped.

Volume formula of a parallelepiped:

V = Ab · h

where V - volume of the parallelepiped,
Ab - the area of the base of the parallelepiped,
h - the height of the parallelepiped.

Volume of a Rectangular Prism

Rectangular Prism

The volume of a rectangular prism is equal to the product of its length, width and height.

Volume formula of a rectangular prism:

V = a · b · h

where V - volume of a rectangular prism,
a - length,
b - width,
h - height.

Volume of a Pyramid

Pyramid

The volume of a pyramid is equal to one third of the product of the area of its base times the height.

The volume formula of a pyramid:


V = 1 Ab · h
3

where V - the volume of a pyramid,
Ab - the area of the pyramid base,
h - the height of the pyramid.

Volume of a Tetrahedron

Tetrahedron

Volume formulas of a tetrahedron:


V = a32
12


where V - volume of a tetrahedron,
a - edge length.


Volume of a Right Circular Cylinder

Circular Cylinder

Volume of a right circular cylinder is equal to the product of the area of its base times the height.

Volume formula of a right circular cylinder:
  • V = π R2 h
  • V = Ab h
where V - volume of a cylinder,
Ab - area of the base,
R - radius of the base,
h - height,
π = 3.141592.

Volume of a Right Circular Cone

Cone

Volume of a right circular cone is equal to one third of the product of the area of its base times the height.

Volume formula of a right circular cone:

V = 1 π R2 h
3

V = 1 Ab h
3

where V - volume of a cone,
Ab - area of the base,
R - radius of the base,
h - height,
π = 3.141592.


Volume of a Sphere (Solid)

Sphere

Volume of a sphere is equal to four-thirds of its radius cubed multiplied by the number pi.

Volume formula of a sphere (solid):


V = 4π R3
3

where V - volume of a sphere,
R - radius of a sphere,
π = 3.141592.


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