Final answer:
To convert the density of helium from kg/m³ to lb/ft³, multiply the given density by the conversion factor from kilograms to pounds, and then divide by the conversion factor for cubic meters to cubic feet, resulting in a density of approximately 0.01024 lb/ft³.
Step-by-step explanation:
The question involves converting the density of helium from kilograms per cubic meter (kg/m³) to pounds per cubic foot (lb/ft³). The student provided the density of helium as 0.164 kg/m³ and the conversion for meters to feet as 1 m = 3.28 ft. Additionally, the conversion factor from kilograms to pounds is 1 kg = 2.20462 pounds.
To convert the density from kg/m³ to lb/ft³, we can use the following steps:
- Convert the mass from kilograms to pounds.
- Convert the volume from cubic meters to cubic feet by raising the linear conversion factor (meters to feet) to the power of three, since we're dealing with cubic units.
Step 1: Convert the density from kg/m³ to lb/m³ by multiplying 0.164 kg by the conversion factor:
0.164 kg/m³ * 2.20462 lb/kg = 0.3616 lb/m³
Step 2: Convert from m³ to ft³:
Since (1 m) ³ = (3.28 ft) ³, then we have:
1 m³ = 3.28³ ft³ = 35.3147 ft³
Now, divide the density in lb/m³ by the cubic conversion factor:
0.3616 lb/m³ / 35.3147 ft³/m³ = 0.01024 lb/ft³
Therefore, the density of helium is approximately 0.01024 lb/ft³.