Unit conversion using dimensional analysis is performed by multiplying the given unit with the conversion factor
The volume of a 2 ft.³ in cubic meters is approximately 0.056634 m³
The given mass of the sample of metal, m = 950 pounds
The units of density using the imperial units = [tex]lb_m[/tex]/ft.³
The units of the volume of the metal sample based on the above density = Cubic feet
The desired units = Cubic meters
The conversion factor for converting a unit in cubic feet to a unit in cubic meters is presented as follows
1 ft.³ = 0.0283 m³
Therefore, using dimensional analysis, the volume quantity in cubic feet is multiplied by 0.0283 m³/(1 ft.³) to convert the volume to cubic meters
Example;
Given that the volume of the metal sample 2 ft.³, we have that the volume in cubic meters is therefore;
2 ft.³ × (0.0283 m³)/(1 ft.³) ≈ 0.056634 m³
The volume of a sample of metal that is 2 ft.³ in cubic meters is ≈ 0.056634 m³
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