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← Volume and Surface Area of Prisms

Rule

Volume of a Cube

Consider a cube with a side length

s .

The volume $V$ of the cube can be calculated by raising the side length $s$ to the power of $3,$ or cubing it.

$V = s^{3}$

Proof

The volume of a prism is calculated by multiplying the area of one base by the height. For rectangular prisms, this value is found by multiplying the area of the rectangular base by the height of the prism.

Volume of a Rectangular Prism {V = B \cdot h B = ℓ \cdot w \Rightarrow V = ℓ \cdot w \cdot h

A square is a special type of rectangle whose length and width are equal, so the area of a square is found by calculating the square of the side length. Similarly, a cube is a special type of rectangular prism whose length, width, and height are equal.

The formula for the volume of a cube can therefore be derived by substituting

s

into the standard equation for the volume of a rectangular prism.

V = ℓ \cdot w \cdot h

SubstituteValues

Substitute values

V = s \cdot s \cdot s

ProdToPowThreeFac

$a \cdot a \cdot a = a^{3}$

V = s^{3}

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Proof