# What Are The Common Mathematical Formulas For Volume?

fact-finder | (Level 3) Valedictorian

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For many geometric figures, the formula for volume is simply: "base area times height," or some fraction thereof. Base area is represented by the capital letter "B." The height of an object is a line perpendicular to the base, equal to the distance from the vertex (highest point) to the base. "Volume" is the space within a three-dimensional object and is expressed in cubic units, such as cubic inches. (Note: pi, represented by the symbol "Π," equals approximately 3.14.)

Volume of a cylinder (with circular base):

Volume = pi times the square of the radius of the base times the height

Since pi times the square of the radius is equal to the area of the base of the cylinder, this formula can also be written as:

Volume of a cube:

Volume = the length of one side cubed

It's also possible to calculate the volume of a cube by finding the area of the base (s2) and multiplying it by the height (also equal to "s")

Volume of a rectangular solid: (Has two parallel bases which are congruent, meaning they have equal sides and equal angles).

Volume = base area times height or Vrectangular solid = Bh

(Note that base area is equal to a x b.)

Volume of a cone: (Note that the volume of a cone is merely one-third that of a cylinder.)

Volume = 1/3 times pi times the square of the radius of the base times the height

(Note that base area equals Π x r2.)

This can be represented as base times height.

Volume of a pyramid:

Volume = times the area of the base times the height

(Note that base area equals a x b.)

Volume of a sphere:

Volume =4/3 times pi times the cube of the radius

Sources: Gibson, Carol. The Facts On File Dictionary of Mathematics, Rev. ed., pp. 46, 49, 150, 172; Stein, Edwin I. Arithmetic for College Students, Rev. ed., pp. 265-69.