Given that water has a density of approximately 1000 kg/m^3 and the total volume of Earth's oceans is about 1.35 × 10^9 km^3, estimate the mass of Earth's oceans in kilograms.

• A. 1.35 × 10^{18} kg
• B. 1.35 × 10^{21} kg
• C. 1.35 × 10^{15} kg
• D. 1.35 × 10^{24} kg

Answer: (B)

Verified step by step guidance

1. Identify the given values: density of water \(\rho = 1000\ \text{kg/m}^3\) and volume of Earth's oceans \(V = 1.35 \times 10^9\ \text{km}^3\).
2. Convert the volume from cubic kilometers to cubic meters because the density is given in kg/m³. Use the conversion factor \$1\ \text{km}^3 = (1000\ \text{m})^3 = 10^9\ \text{m}^3$.
3. Calculate the volume in cubic meters by multiplying the given volume by \$10^9\(: \)V_{m^3} = 1.35 \times 10^9 \times 10^9 = 1.35 \times 10^{18}\ \text{m}^3$.
4. Use the formula for mass based on density and volume: \(m = \rho \times V\).
5. Multiply the density by the converted volume to estimate the mass of Earth's oceans: \(m = 1000\ \text{kg/m}^3 \times 1.35 \times 10^{18}\ \text{m}^3\).