Recently one month's production of sodium hydroxide in the US was 2.21 billion pounds. The density of sodium hydroxide is 2.130 g/cm³. How many cubic kilometers were produced?
To calculate the volume of sodium hydroxide produced in cubic kilometers, we need to convert the mass from pounds to grams, and then divide it by the density of sodium hydroxide.
1 pound is equal to 0.453592 kg.
1 kilogram is equal to 1000 grams.
So, the mass in grams can be calculated as follows:
Mass (grams) = 2.21 billion pounds * 0.453592 kg/pound * 1000 g/kg.
Next, we can calculate the volume in cubic centimeters (cm³) by dividing the mass by the density:
Volume (cm³) = Mass (g) / Density (g/cm³).
Finally, to get the volume in cubic kilometers, we need to convert the volume from cm³ to km³.
1 kilometer is equal to 100,000 centimeters.
So, the volume in cubic kilometers can be calculated as:
Volume (km³) = Volume (cm³) / (100000 cm/km)^3.
Let's plug in the numbers and calculate it step by step:
Mass (grams) = 2.21 billion pounds * 0.453592 kg/pound * 1000 g/kg
= 2.21 * 10^9 * 0.453592 * 10^3 g
= 1.00 * 10^12 g
Volume (cm³) = Mass (g) / Density (g/cm³)
= 1.00 * 10^12 g / 2.130 g/cm³
= 4.69 * 10^11 cm³
Volume (km³) = Volume (cm³) / (100000 cm/km)^3
= 4.69 * 10^11 cm³ / (100000 cm/km)^3
≈ 4.69 * 10^-3 km³
Therefore, approximately 4.69 * 10^-3 cubic kilometers of sodium hydroxide were produced.