The density of water is 1 g/cm^3. What is this value in kg/m^3?

• A. 0.1 kg/m^3
• B. 1 kg/m^3
• C. 1000 kg/m^3
• D. 10 kg/m^3

Answer: (C)

Verified step by step guidance

1. Identify the given density and its units: 1 g/cm^3.
2. Recall the unit conversions: 1 g = 0.001 kg and 1 cm = 0.01 m.
3. Convert the volume units from cm^3 to m^3 by cubing the length conversion: (1 cm)^3 = (0.01 m)^3 = 1 \times 10^{-6} m^3.
4. Express the density in kg/m^3 by converting grams to kilograms and cubic centimeters to cubic meters using the formula: \(\text{density in kg/m}^3 = \frac{1 \text{ g}}{1 \text{ cm}^3} \times \frac{0.001 \text{ kg}}{1 \text{ g}} \times \frac{1}{1 \times 10^{-6} \text{ m}^3}\).
5. Simplify the expression to find the density in kg/m^3.