1. Identify the given values and conversion factors: - Density: [tex]\( \frac{2350 \text{ kg}}{1 \text{ m}^3} \)[/tex] - Conversion factor from kilograms to pounds: [tex]\( 2.2 \frac{\text{lb}}{\text{kg}} \)[/tex] - Conversion factor from cubic meters to cubic feet: [tex]\( \frac{1 \text{ m}^3}{35.3 \text{ ft}^3} \)[/tex]
2. Set up the equation using the given conversions: [tex]\[
\frac{2350 \text{ kg}}{1 \text{ m}^3} \times \frac{2.2 \text{ lb }}{1 \text{ kg}} \times \frac{1 \text{ m}^3}{35.3 \text{ ft}^3}
\][/tex]
3. Perform the multiplications and cancellations: - First, multiply the density in kg per m³ by the conversion factor to pounds: [tex]\[
2350 \text{ kg/m}^3 \times 2.2 \text{ lb/kg} = 5170 \text{ lb/m}^3
\][/tex]
- Next, divide by the conversion factor to cubic feet: [tex]\[
5170 \text{ lb/m}^3 \times \frac{1 \text{ m}^3}{35.3 \text{ ft}^3} = \frac{5170 \text{ lb}}{35.3 \text{ ft}^3}
\][/tex]
4. Calculate the final result: - Perform the division: [tex]\[
\frac{5170 \text{ lb}}{35.3 \text{ ft}^3} \approx 146.4589235127479 \text{ lb/ft}^3
\][/tex]
Thus, the density [tex]\( \frac{2350 \text{ kg}}{1 \text{ m}^3} \)[/tex] is approximately equal to [tex]\( 146.4589235127479 \text{ lb/ft}^3 \)[/tex].
