The density of water is 1 gram per cubic centimeter (
). Express this (a) in kilogram per cubic meter (
) and (b) in pound per cubic feet (
). Note: 1 lb = 454 g
The Correct Answer and Explanation is:
The given density of water is:
1 gram per cubic centimeter (g/cm³)
(a) Convert to kilogram per cubic meter (kg/m³)
We use the following conversion factors:
- 1 g = 0.001 kg
- 1 cm³ = 0.000001 m³ (since 1 m=100 cm⇒1 m3=106 cm31\,\text{m} = 100\,\text{cm} \Rightarrow 1\,\text{m}^3 = 10^6\,\text{cm}^31m=100cm⇒1m3=106cm3)
So:1 g/cm3=1 g1 cm3=0.001 kg0.000001 m3=1000 kg/m31\,\text{g/cm}^3 = \frac{1\,\text{g}}{1\,\text{cm}^3} = \frac{0.001\,\text{kg}}{0.000001\,\text{m}^3} = 1000\,\text{kg/m}^31g/cm3=1cm31g=0.000001m30.001kg=1000kg/m3
Answer: 1000 kg/m³
(b) Convert to pound per cubic foot (lb/ft³)
We use the following conversion factors:
- 1 lb = 454 g
- 1 ft = 30.48 cm → 1 ft3=(30.48)3 cm3=28316.8466 cm31\,\text{ft}^3 = (30.48)^3\,\text{cm}^3 = 28316.8466\,\text{cm}^31ft3=(30.48)3cm3=28316.8466cm3
We start from:1 g/cm3=1 g1 cm31\,\text{g/cm}^3 = \frac{1\,\text{g}}{1\,\text{cm}^3}1g/cm3=1cm31g
Now convert grams to pounds:1 g=1454 lb1\,\text{g} = \frac{1}{454}\,\text{lb}1g=4541lb
So:1 g/cm3=1454 lb/cm31\,\text{g/cm}^3 = \frac{1}{454}\,\text{lb/cm}^31g/cm3=4541lb/cm3
Now convert cm³ to ft³:1 lb/cm3=28316.8466 lb/ft31\,\text{lb/cm}^3 = 28316.8466\,\text{lb/ft}^31lb/cm3=28316.8466lb/ft3
So:1454 lb/cm3=28316.8466454 lb/ft3≈62.36 lb/ft3\frac{1}{454}\,\text{lb/cm}^3 = \frac{28316.8466}{454}\,\text{lb/ft}^3 \approx 62.36\,\text{lb/ft}^34541lb/cm3=45428316.8466lb/ft3≈62.36lb/ft3
Answer: Approximately 62.36 lb/ft³
Explanation
Density is a measure of mass per unit volume. The density of pure water at 4°C is 1 gram per cubic centimeter. This unit is commonly used in scientific contexts, but practical and engineering applications often require conversions to other systems such as SI (International System of Units) or imperial units.
To convert to kilograms per cubic meter, we recognize that 1 kilogram contains 1000 grams, and 1 meter contains 100 centimeters. Therefore, 1 cubic meter equals 1 million cubic centimeters. When we apply these conversions, we see that 1 gram per cubic centimeter translates to 1000 kilograms per cubic meter. This is a standard reference value in physics, chemistry, and environmental science.
To express the same density in imperial units such as pounds per cubic foot, we need to convert both the mass and the volume. One pound equals 454 grams, and one cubic foot equals 28316.8466 cubic centimeters. By converting the units accordingly, we find that 1 gram per cubic centimeter is approximately 62.36 pounds per cubic foot. This value is frequently used in civil engineering, construction, and HVAC (heating, ventilation, and air conditioning) calculations when dealing with water or fluids of similar density.
Understanding how to convert units of density allows scientists and engineers to apply standard data in various systems and ensures consistency in calculations across international boundaries and disciplines.
