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The Dimensional Analysis Rule for Volume
Linear unit conversion factors must be cubed when converting volumetric units:
- $1 ext{ m} = 100 ext{ cm} \implies 1 ext{ m}^3 = 100^3 = \mathbf{1,000,000 ext{ cm}^3}$.
- $1 ext{ ft} = 12 ext{ in} \implies 1 ext{ ft}^3 = 12^3 = \mathbf{1,728 ext{ in}^3}$.
- $1 ext{ yd} = 3 ext{ ft} \implies 1 ext{ yd}^3 = 3^3 = \mathbf{27 ext{ ft}^3}$.